GIFT  OF 
Dr.   Horace  I vie 


• 


PLATE  1 


Lith. Co  Boston 


THE 


PRINCIPLES   OF   PHYSICS 


ALFRED   P.  GAG$,  PH.D.  ,  \ 

AUTHOR  OF  "ELEMENTS  OF  PHYSICS,','  •'',ISTT^'>I'IUCTTON'I'Q' 
PHYSICAL  SCIENCE,"  ETC. 


BOSTON,  U.S.A.,  AND  LONDON 

GINN     &     COMPANY,    PUBLISHERS 

1895 


,  ENTBREW  AT  STATIONERS'  HALL 


COPYRIGHT,  1895 


I  k«r  :*J.' '•'*•*     :  ifc  ALFRED  p.  GAGE 


vi  c. 
EDUCATJON 


PREFACE. 


IT  is  now  thirteen  years  since  my  Elements  of  Physics  was 
published.  In  the  interim  many  changes  in  the  technical  no- 
menclature of  Physics  and  many  improvements  in  methods  of 
presentation  of  portions  of  the  science  have  been  made,  and, 
above  all,  the  whole  subject  of  Electricity  and  Magnetism  has 
outgrown  its  former  apparel.  Furthermore,  the  present  is 
conceded  to  be  an  era  of  extraordinary  scientific  activity,  and 
the  demand  for  frequent  revisions  of  scientific  text-books  is 
correspondingly  imperative. 

The  present  volume,  however,  is  a  new  work,  and  not  a 
mere  revision  of  former  works.  Much  of  the  material  of 
previous  works,  when  suited  to  present  needs,  has  naturally 
been  incorporated  into  this  ;  but  everything  has  been  carefully 
rewritten  and  rearranged  with  reference  to  its  adaptability  to 
the  requirements  of  the  present  day. 

The  considerable  increase  of  volume  and  scope  of  this  work 
over  those  of  its  predecessors  may  require  some  explanation. 
In  this  book  I  have  naturally  been  moved  to  attempt  to  meet 
the  demands  of  many  highly  esteemed  critics  who  have  com- 
plained of  serious  omissions  in  my  former  works,  and  I  am 
apprehensive  solely  lest  this  volume  also  may  fall  short  of  the 
requirements  of  many.  Then,  too,  as  was  suggested  above,  the 
scientific  activity  of  this  age  results  in  successive  additions 
both  to  the  theory  of  Physics  and  to  its  application,  and  thus 
tends  to  make  the  ground  covered  by  new  text-books  con- 
tinually greater. 


IV  PREFACE. 

** 

But  this  book  represents  more  than  this  :  it  represents  the 
author's  protest  against  a  tendency  in  some  quarters  towards 
demanding  " smaller  books,"  "cheaper  books,"  " primers  of  sci- 
ence,"—  a  protest  based  on  the  conviction  that  true  education 
does  not  consist  in  the  acquisition  of  the  fewest  possible  facts 
about  any  subject.  Education,  in  Physics,  implies  the  presen- 
tation of  the  great  truths  of  that  science  in  their  unmutilated 
form,  the  indication  of  their  relations  to  one  another,  and  the 
furnishing  the  student  an  opportunity  of  observing  and  exercis- 
ing the  logical  processes  that  have  led  to  the  discpvery  of  those 
truths.  Any  text-book  that  aims  to  introduce  the  student 
to  a  study  of  such  importance  and  such  inexhaustible  possibili- 
ties should  not  lose  sight  of  this  truth  and  encourage  mere 
dilettanteism.  In  particular  there  is  needed  a  store  of  illustra- 
tive matter,  of  concrete  applications  of  general  principles, 
sufficient  to  make  clear  those  principles  and  to  indicate  the 
inductive  processes  by  which  they  have  been  reached  and  the 
deductions  to  which  they  lead. 

Meagre  information  results  in  hazy  comprehension,  and 
consequently  provokes  but  meagre  interest.  Full  and  varied 
treatment,  on  the  contrary,  by  presenting  different  points  of 
view,  clears  the  conceptions  and  thus  provokes  interest,  and 
allures  to  continued  study.  All  things  considered,  too  much 
in  a  text-book  is  far  preferable  to  too  little. 

In  these  considerations'  may  be  found  a  partial  explanation 
of  the  size  of  this  volume  :  a  work  which  aims  to  afford  the 
possibility  and  the  incentive  to  more  than  a  superficial  know- 
ledge of  the  subject. 

The  work  contains  two  courses — one  which  is  termed  a  high 
school  course,  and  the  other  an  advanced  course.  The  former  is 
printed  in  larger  type  ;  the  latter  comprises  the  former  and 
additional  matter  printed  in  smaller  type,  which  is  indented 
about  one-fourth  of  an  inch  at  the  left  margin  of  the  page. 
The  former  embraces  a  full  course  for  those  high  schools  and 


PREFACE.  V 

academies  which  are  able  to  do  a  fairly  good  work.  This 
course  can  be  abbreviated  at  the  option  of  teachers  as  neces- 
sity may  require. 

While  the  advanced  course  does  not  aspire  to  meet  the 
requirements  of  a  technical  scientific  course  in  the  higher  insti- 
tutions, yet  it  is  believed  that,  supplemented  by  lectures,  as 
all  text-books  should  be  in  the  higher  institutions,  it  may  meet 
the  requirements  of  the  so-called  classical  courses  in  many 
colleges.  In  the  high  school  it  provides  a  way  for  pupils 
possessed  of  a  special  genius  and  aptitude  for  scientific  studies 
to  delve  deeper  into  many  subjects  than  the  average  pupil  is 
wont  to  do. 

This  work  is  simply  a  text-book.  It  lays  no  claim  to  be  a 
laboratory  manual.  It  is  expected  that  its  teachings  will  be 
supplemented  by  laboratory  work,  for  laboratory  practice  has 
come  to  be  considered  an  essential  part  of  every  scientific 
course.  Experiments  are  introduced  chiefly  for  the  purpose 
of  illustrating  principles  and  laws,  but  tedious  details  which 
would  tend  to  distract  the  attention  from  the  leading  facts 
have  been  omitted. 

I  take  this  opportunity  to  acknowledge  the  debt  I  owe  to 
many  able  physicists  and  representative  instructors  for  advice 
and  help.  My  special  thanks  are  due  to  my  friend,  Dr.  Arthur 
W.  Goodspeed,  of  the  University  of  Pennsylvania,  for  very 
many  valuable  suggestions  and  contributions,  and  for  careful 
reading  both  of  the  manuscript  and  the  proof-sheets.  Both 
manuscript  and  proof-sheets  have  also  been  critically  read  by 
Prof.  Joseph  0.  Thompson,  of  Amherst  College,  and  my  col- 
league, Mr.  A.  P.  Walker,  of  the  English  High  School,  Boston. 
To  the  former  I  am  under  special  obligations  for  much  valu- 
able assistance,  and  to  the  latter  I  am  largely  indebted  for 
whatever  freedom  from  rhetorical  and  typographical  errors 
this  book  may  possess. 

For  valuable  criticism  of  proof-sheets,  I  have  also  to  record 


VI  PREFACE. 

my  warm  personal  thanks  to  Dr.  Daniel  W.  Herring,  of  the 
University  of  the  City  of  New  York ;  Dr.  J.  S.  McKay,  of 
the  Packer  Collegiate  Institute,  Brooklyn ;  Mr.  C.  F.  Adams, 
Detroit  High  School  ;  Mr.  A.  J.  Rogers,  Milwaukee  High 
School ;  Prof.  J.  W.  Moore,  Lafayette  College,  Easton,  Pa. ; 
Mr.  J.  T.  Coleman,  Citadel  Academy,  Charleston,  S.  C.  ;  Mr. 
A.  D.  Gray,  Penn  Charter  School,  Philadelphia ;  and  Mr. 
William  Orr,  Springfield  (Mass.)  High  School.  The  General 
Electric  Company  and  the  Zeigler  Electric  Company  have 
kindly  furnished  several  cuts  of  electrical  machinery  and 
other  apparatus. 

A  key  to  the  solution  of  problems  and  exercises  contained 
in  this  book  will  be  furnished  by  the  publishers  to  those  in- 
structors only  who  use  this  as  their  regular  text-book. 

A.  F.  G. 


CONTENTS. 


INTRODUCTION. 

PAGE 

Fundamental  units  of  measurements.  Kinematics.  Motion,  velocity, 
acceleration.  Laws  of  accelerated  motion.  Composition  and  reso- 
lution of  velocities.  Kinds  of  motion 1-32 


PART    I. 
MOLAR  DYNAMICS. 

CHAPTER  I. 

Force  and  momentum.  Measurement  of  force.  Composition  and 
resolution  of  forces.  Moments  of  forces.  Center  of  mass.  New- 
ton's Laws  of  Motion.  Curvilinear  motion.  The  pendulum.  Work, 
energy,  and  activity.  Machines 33-117 

CHAPTER  II. 
Gravitation 118-123 

CHAPTER  III. 

Properties  of  matter.  Constitution  of  matter.  States  of  matter.  Mo- 
lecular forces.  Capillarity.  Diffusion  of  fluids 124-141 

CHAPTER  IV. 

Dynamics  of  fluids.  Transmission  of  pressure.  Atmospheric  pres- 
sure. Boyle's  Law.  Instruments  for  rarefying  air.  Siphons  and 
pumps.  Buoyancy  of  fluids.  Density  and  Specific  density  ...  142-185 


Vlll  CONTENTS. 


CHAPTER  V. 

PAGE 

Energy  of  mass-vibration.  Sound-waves.  Speed  of  sound-waves. 
Energy  of  sound-waves.  Reflection  and  refraction  of  sound-waves. 
Reenforcement  and  interference  of  sound-waves.  Pitch  of  musical 
sounds.  Composition  of  sonorous  vibrations.  Vibration  of  strings. 
Harmony  and  discord.  Quality  of  sound.  Analysis  and  synthesis 
of  sound-waves.  Musical  instruments.  Vocal  organs.  The  ear  .  180-244 


PART    II. 

MOLECULAR   DYNAMICS.    HEAT. 

Theory  of  heat.  Sources  of  heat.  Temperature.  Thermometry. 
Calorimetry .  Effects  of  heat :  Expansion.  Kinetic  theory  of  mat- 
ter. Laws  of  gaseous  bodies.  Absolute  temperature.  Fusion. 
Vaporization.  Methods  of  producing  cold  artificially.  Hygrom- 
etry.  Diffusion  of  heat.  Therm o-dynamics.  Steam-engine  .  .  .  245-314 


PART    III. 

ETHER  DYNAMICS. 

CHAPTER  I. 

Radiant  energy.  Light.  Speed  of  light.  Intensity  of  illumination. 
Apparent  size  of  an  object.  Reflection  of  light.  Refraction.  Prisms 
and  lenses.  Prismatic  analysis  of  light.  Color.  Interference  and 
diffraction.  Double  refraction  and  polarization.  Thermal  effects 
of  radiation.  Optical  instruments 315-433 

CHAPTER  II. 

Electrostatics.  Electrification.  Induction.  Distribution  of  elec- 
tricity. Electrical  potential.  Electrical  machines.  Electrostatic 
lines  of  force.  Atmospheric  electricity 434-461 

CHAPTER  III. 

Electrokinetics.  Voltaic  batteries.  Some  defects  of  batteries.  Ef- 
fects produced  by  the  current.  Electrical  quantities  and  units, 


CONTENTS.  ix 


Electrostatic  units.  Rules  relating  to  an  electric  current.  Instru- 
ments for  electrical  measurements.  Resistance  of  conductors. 
Measurement  of  resistance.  E.  M.  F.  of  different  cells.  Divided 
circuits.  Methods  of  combining  voltaic  cells.  Verification  of 
Ohm's  Law.  Magnets  and  magnetism.  Magnetic  lines  of  force. 
The  magnetic  circuit.  Terrestrial  magnetism.  Magnetic  relations 
of  the  current.  Electro-magnets.  Electro-dynamics.  Ampere's 
theory  of  magnetism.  Electro-magnetic  induction.  Dynamo-electric 
machines.  Electric  motor.  The  transformer.  Storage  batteries. 
Electrical  transmission  of  activity.  Thermo-electric  currents. 
Electro-magnetic  theory  of  light.  Electric  radiation.  Electric 
light.  Electrotyping  and  electroplating.  Telegraphy.  Telephony. 
The  bolometer.  Alternating  currents.  Tesla's  investigations  .  .  462-608 


PRINCIPLES  OF         YSIC8.;\  % 


INTRODUCTION. 


FUNDAMENTAL    UNITS    OF    MEASUREMENT. 

ACCURATE  knowledge  of  physical  phenomena  is  obtained 
only  by  means  of  precise  measurements  of  physical  quan- 
tities. 

1.  Quantity  is  that  attribute  of  things  which  makes  them 
measurable,  i.e.  it  is  that  which  answers  the  questions  How 
much  ?    How  great  ?  —  etc.     A  quantity  is  therefore  a  meas- 
urable portion  of  anything. 

A  physical  measurement  consists  in  finding  how  many  times 
a  definite  quantity,  called  a  unit,  is  contained  in  the  quantity 
to  be  measured.  Such  a  unit  which  has  become  legalized, 
either  by  statute  or  by  common  usage,  is  called  a  standard 
unit. 

The  expression  of  a  physical  quantity  consists  of  a  state- 
ment of  the  concrete  unit  employed,  e.g.  pound,  foot,  quart, 
etc.,  with  the  number  of  those  units  prefixed.  The  numerical 
part,  called  the  numeric,  is  obtained  by  measurement. 

2.  The  fundamental  units,  in  terms  of  which  all  physical 
measurements  are  made,  are  those  of  length,  mass,  and  time.1 
These  are  fundamental  in  the  sense  that  no  one  is  derivable 

1  "  The  whole  system  of  civilized  life  may  be  fitly  symbolized  by  a  foot  rule,  a  set 
of  weights,  and  a  clock."  Maxwell. 


2  FUNDAMENTAL    UNITS    OF    MEASUKEMENT. 

from  others.  The  three  entities  which  these  units  measure 
cannot  be  absolutely  defined ;  but,  fortunately,  they  are  too 
familiar  to  require  definition. 

The'  ui.'it  of .  length  (or  "space  of  one  dimension")  is  the 
meter  (metric1),  or  yard  (British).  The  centimeter  (see  p.  617) 
is  the  one-huiidred'th  part  of  a  meter.  A  standard  meter  is 
defined  by  law  (1795)  to  be  the  shortest  distance  between  the 
ends  of  a  platinum  rod  (made  by  Borda  and  called  Metre  des 
Archives)  at  0°  C.  This  rod  is  in  the  keeping  of  the  Academy 
of  Sciences  at  Paris. 

The  foot  is  one-third  of  the  British  standard  yard.  The 
yard  is  denned  by  act  of  Parliament  (1855)  to  be  the  dis- 
tance between  the  intersections  of  the  transverse  lines  in 
two  gold  plugs  in  a  bronze  bar  deposited  at  the  office  of  the 
Exchequer  in  London,  the  temperature  of  the  bar  being 
62°  F.  (16§°  C.). 

3.  By  the  mass  of  a  body  is  meant  the  quantity  of  matter 
contained  in  the  body.  It  is  highly  important  to  bear  in 
mind  that  the  idea  implied  in  the  term  mass  is  quite  distinct 
from  that  of  weight.  The  weight  of  a  body  changes  with  its 
distance  from  the  earth,  while  its  mass  remains  the  same. 
The  weight  of  a  body  is  the  measure  of  the  attraction  between 
it  and  the  earth,  and  is  variable  because  the  attraction  of  the 
earth  differs  at  different  places,  but  its  mass  is  not  affected  by 
this  attraction. 

The  unit  of  mass  generally  employed  in  science  is  the  gram 
or  the  pound.  The  gram  is  the  one-thousandth  part  of  the 
standard  kilogram.  This  standard  is  a  piece  of  platinum, 
called  the  Kilogramme  des  Archives,  carefully  preserved  by  the 

1  The  metric  system  (see  page  617)  is  now  generally  employed  in  scientific  work. 
The  advantage  of  this  system  consists  largely  in  the  simplicity  of  the  relations  which 
exist  between  the  standards  of  length  and  mass,  and  in  the  use  of  units  each  of 
which  is  some  decimal  multiple,  or  sub-multiple,  of  the  others  in  the  same  series. 
"The  British  measurements  are  infinitely  inconvenient  and  wasteful  of  brain- 
energy."  Tait.  —  "I  look  upon  our  English  system  as  a  wickedly  brain-destroying 
piece  of  bondage  under  which  we  suffer."  Lord  Kelvin. 


PROCESS    OF    MEASURING    MASS.  6 

French  Government  at  Paris.  Originally  it  was  intended  to 
represent  the  mass  of  a  cubic  decimeter  of  pure  water  at  the 
temperature  of  4°  C.  A  kilogram  of  any  substance  is  that 
quantity  of  the  substance  which,  placed  on  a  scale  pan,  would 
just  balance  in  a  vacuum  the  standard  kilogram  placed  on  the 
other  pan. 

The  English  unit  of  mass  is  defined  by  act  of  Parliament 
(1855)  to  be  a  piece  of  platinum  marked  "P.  S.,  1  lb.," 
denominated  the  Imperial  Standard  Pound  Avoirdupois.  It 
is  deposited  in  the  office  of  the  Exchequer. 

The  process  of  measuring  the  mass  of  a  body  by  balancing- 
it  with  a  body  or  bodies  of  known  mass  is  called  weighing. 
The  process  of  weighing,  as  commonly  understood,  is  essen- 
tially a  comparison  of  masses.  A  set  of  masses1  (e.g.  a  kilo- 
gram down  to  a  milligram)  consists  .of  a  series  of  bodies 
having  masses  corresponding  to  the  denominations  given  them. 

The  process  of  measuring  the  mass  of  a  body  must  not  be 
confounded  with  the  process  of  finding  how  heavy  a  body  is 
(i.e.  how  great  the  attraction  between  it  and  the  earth  is), 
although  both  processes  are,  in  common  usage,  called  weigh- 
ing. Not  only  are  the  things  measured  in  the  two  cases 
entirely  different,  but  the  instruments  that  may  be  required 
are  quite  different.  For  example,  a  kilogram  mass  always 
has  the  same  mass,  and  may,  therefore,  when  used  with  the 
scale  balance,  be  relied  upon  always  and  everywhere  to 
measure  accurately  an  equal  mass  of  any  body.  But  a  kilo- 
gram mass  when  suspended  from  a  spring  balance  may  be 
found  to  be  heavier  in  certain  situations  than  in  others,  hence 
this  instrument  does  not  under  all  circumstances  measure 
mass  correctly.  On  the  other  hand,  the  scale  balance  will 
not  detect  any  change  in  the  heaviness  of  a  kilogram  mass  ; 
hence  this  instrument  does  not  always  measure  heaviness 
correctly.  For  most  practical  purposes,  however,  these  in- 

1  Commonly  called  a  set  of  weights. 


FUNDAMENTAL    UNITS    OF    MEASUREMENT. 

struments  may  be  used  interchangeably,  inasmuch  as  at  the 
same  place  mass  is  proportional  to  weight.1 

The  unit  of  time  generally  employed  in   scientific  meas- 
urement is  the  second.     The  second  is    Q    * » „   of  the  mean 

o  b  4:  U  U 

solar  day. 

4.  Derived  units ;    C.   G.  S.  System.  —  The  system  of   measure- 
ments in  which  all  the  units  used  in  measuring  physical  quantities 
are  derived  from  the  three  metric  units  given  above  is  called  the 
centimeter-gram-second  system,   or,   briefly,   the  C.    G.   S.  system. 
The  system  is  also  called  an  absolute  system  of  units. 

In  any  absolute  system  the  unit  of  length  is  represented  symbol- 
ically by  [L],  that  of  mass  by  [M],  and  that  of  time  by  [T].  Any 
derived  unit  may  be  represented  by  certain  powers  of  these  symbols, 
or  by  the  product  of  certain  powers  of  these  symbols.  Thus  the 
unit  of  area  =  [L2]. 

5.  Dimensional  equations.  —  Any  equation  showing  what  powers 
of  the  fundamental  units  enter  into  the  expression  for  the  derived 
unit,  is  called  its  dimensional  equation.     The  dimensional  equation 
for  any  derived  unit  is  deduced  from  the  physical  laws  by  which 
the  unit  is  defined. 

6.  Volume.  —  By  the  volume  of  a  body  is  meant  the  quan- 
tity of  space  it  occupies.     The  derived  unit  of  measurement 
of  volume  is   the  cubic  centimeter   (or  cubic  foot),   and  is 
defined  as  the  volume  of  a  cube  the  length  of  one  side  of 
which  is  one  centimeter. 

The  dimensional  equation  for  volume  is  (V)  =  [L8]. 

7.  Matter,  body,  substance.  —  Provisionally  we  may  define 
matter2  as  that  which  occupies  space.     A  body  is  any  limited 

1  This  is  one  of  many  instances  in  physics  in  which  one  quantity  is  indirectly 
measured  by  measuring  another  proportional  to  it.    Legitimately  speaking  it  is  not 
the  function  of  a  spring  balance  to  measure  mass,  nor  of  the  scale  balance  to 
measure  heaviness.    The  first  measures  stress  (§  63) ;  and  the  second  demonstrates 
equality  of  moments  (§  50). 

2  Matter  is  variously  defined  in  scientific  text-books  according  to  the  fancy  of  the 
authors.    The  definitions  are,  however,  only  provisional,  serving  merely  the  practical 
requirement  of  distinguishing  between  what  is  matter  and  what  is  not  matter.    The 
question  "What  is  matter?"  is  still  a  subject  of  pure  speculation,  and  its  discussion 
therefore  wholly  unsuited  to  a  scientific  text-book.    The  discovery  of  its  ultimate 


PHYSICAL  PHENOMENA  AND  PHYSICAL  LAWS.     5 

portion  of  matter,  e.g.  a  lake,  a  tumbler,  a  desk,  etc.  Names 
of  bodies  should  be  carefully  distinguished  from  names  of 
substances  which  indicate  merely  the  kind  of  matter  of  which 
the  bodies  are  composed,  such  as  water,  glass,  wood,  etc. 

8.  Phenomena,  physical  laws.  —  By  observation  we  learn 
that  a  piece  of  iron  expands  when  heated,  begins  to  be 
luminous  when  heated  to  a  certain  temperature,  and  changes 
to  a  liquid  when  heated  much  more.  Here  are  three  distinct 
changes  which  heat  may  effect.  Changes  or  events  like  these, 
and  countless  others  which  occur  in  nature,  are  called  physical 
phenomena. 

If,  after  many  trials  with  iron  from  various  sources  and 
under  varying  conditions,  we  are  able  to  state  in  general  that 
the  application  of  heat  in  suitable  quantities  to  iron  will  be 
followed  by  these  phenomena,  such  a  generalized  statement  is 
called  a  physical  law.  A  physical  law  is  an  expression  of  a 
constant  relation  which  has  been  discovered  to  exist  between 
certain  physical  quantities. 

Physical  laws,  unlike  statute  and  moral  laws,  do  not  govern 
events,  but  are  generalized  statements  of  the  order  of  events. 
Iron  does  not  expand  in  obedience  to  a  law  that  "  heat  expands." 
We  do  not  explain  why  a  body  falls  to  the  earth  by  stating  a 
law  that  "an  unsupported  body  falls";  indeed,  the  cause  of  a 
fall  has  never  been  discovered,  though  every  one  of  us  has 
individually  discovered  the  law  just  quoted. 

nature  may  be  beyond  the  range  of  human  intelligence.  The  following  attempt  to 
answer  this  question  is  given  (1)  to  illustrate  the  significance  of  the  question  ;  (2)  as 
a  statement  of  the  theory  probably  entertained  at  the  present  time  by  our  most 
advanced  scientists  :  —  "  Matter  is  the  rotating  parts  of  an  inert  perfect  fluid  which 
fills  all  space,  but  which  is,  when  not  rotating,  absolutely  unperceived  by  our  senses." 
Lord  Kelvin. 


KINEMATICS. 


SECTION  I. 

MOTION,    VELOCITY,    ACCELERATION. 

9.  Motion.  —  Kinematics  (from  KLV^^O.,  motion)  treats  of 
motions  without  reference  to  their  causes.  Motion  is  a  con- 
tinuous change  of  position.  The  position  of  a  particle  of 
matter  is  determined  by  its  direction  and  distance  from  another 
particle,  or  from  some  point  of  reference.  A  particle  moves 
relatively  to  a  given  point  while  the  straight  line  con- 
necting it  with  the  point  changes  either  in  direction  or 
length.  A  particle  is  at  rest  relative  to  a  given  point  while 
a  straight  line  joining  them  changes  neither  in  direction  nor 
length. 

While  you  are  opening  or  shutting  the  legs  of  a  pair  of 
dividers  (A,  Fig.  1),  a  straight  line  a'  b'  connecting  the  points 
at  the  ends  of  the  legs  changes  in  length ;  hence  there  is 
relative  motion  between  these  points.  If  (B,  Fig.  1)  you 
open  the  legs  a  little  way,  and,  fixing  the  end  of  one  of  the 
legs  upon  a  plane  surface,  trace  a  circle  with  the  end  of  the 
other  leg  around  the  former  as  a  center,  there  will  be  relative 
motion  between  the  two  points,  since  a  line  joining  them, 
a  b,  ab',  etc.,  changes  in  direction. 

If  (C,  Fig.  1)  you  trace  with  the  points  of  the  open  dividers 
two  straight  parallel  lines  on  a  plane  surface,  the  two  points 
will  be  relatively  at  rest,  just  as  surely  as  if  the  dividers  were 
lying  upon  the  table,  since  in  both  cases' a  straight  line  con- 


RELATIVE    MOTION. 


necting  the  points  a  b,  a'  b\  etc.,  changes  neither  in  length  nor 
in  direction. 

A  point  may  be  at  the  same  instant  at  rest  with  reference 
to  certain  points,  and  in  motion  with  reference  to  certain  other 
points.  For  example,  while  the  points  of  the  dividers  are 
tracing  straight  lines  on  the  plane  surface  (C,  Fig.  1),  and  are 
relatively  at  rest,  they  are  in  motion  with  reference  to  every 
point  in  the  plane  surface. 


a' 


b"      b'" 
FIG.  1. 


When  a  particle  is  spoken  of  as  being  in  motion  or  at  rest,  some 
point  is  always  expressed  or  understood,  relatively  to  which  the 
change  or  permanence  of  position  is  maintained.  All  motions  with 
which  we  have  to  do,  or  which  we  can  measure,  are  relative.  Change 
of  position  with  reference  to  a  fixed  point  in  space  would  be  absolute 
motion.  But  there  is  no  fixed  point  which  we  know.  "  There  are 
no  landmarks  in  space ;  one  portion  of  space  is  exactly  like  every 
other  portion,  so  that  we  cannot  tell  where  we  are"  or  in  what 
direction,  or  how  fast,  we  are  going. 

In  ordinary  language  the  phrase  "a  body  at  rest"  means  that  the 
body  does  not  change  its  position  with  reference  to  that  on  which  it 
stands,  as,  for  instance,  the  surface  of  the  earth  or  the  deck  of  a 


8  KINEMATICS. 

ship.  It  can  mean  nothing  else,  for  both  it  and  all  points  of  the 
earth's  surface  are  in  rapid  motion  with  reference  to  the  sun  and 
other  heavenly  bodies,  and  also  with  reference  to  the  earth's  axis. 

A  body  moves  as  a  whole  with  reference  to  any  point  only 
when  a  certain  point  of  that  body,  called  its  center  of  mass, 
or  centroid,1  changes  its  position  with  reference  to  the  given 
point.  Thus  the  relative  motion  of  two  bodies  is  determined 
by  the  change  of  position  of  their  centroids.  Likewise  the 
path  'in  which  a  body  moves  should  be  understood  to  mean  the 
line  described  by  its  centroid. 

10.  Velocity.  —  No  motion  is  instantaneous.     A  body  con- 
sumes time,  longer  or  shorter,  in  its  transit  from  one  position 
to  another.    Rate  of  change  of  place  (or  time-rate  of  displace- 
ment) of  a  body  is  called  its  velocity.     Velocity  is  expressed  by 
stating  the  number  of  units  of  distance  traversed  in  a  unit  of 
time.     For  scientific  purposes  it  is  most  frequently  expressed 
in  centimeters  per  second ;  for  practical  purposes  the  units  of 
time  and  distance  are  chosen  at  convenience,  as  the  velocity 
of  a  locomotive  in  miles  per  hour,  of  a  rifle  bullet  in  feet  per 
second,  etc.     Observe  that  velocity  is  distance  per  unit  of  time, 
and  cannot  be  correctly  expressed  in  miles,  feet,  etc.,  alone. 

Velocity  involves  the  idea  of  direction,  and  may  change  in 
both  magnitude  and  direction.  It  is  sometimes  convenient  to 
ignore  the  direction  of  a  body's  rate  of  displacement,  in  which 
case  we  use  the  term  speed.  Thus  it  is  better  to  speak  of  the 
speed  of  the  locomotive  and  the  bullet  when  only  the  magnitude 
of  the  change  in  position  is  considered. 

11.  Constant  and  accelerated  velocity.  —  When  a  body  moves 
in  a  straight  line  with  unchanging  rate,  i.e.  when  it  traverses 
equal  spaces  in  equal  times,  its  velocity  is  said  to  be  constant. 
In  case,  however,  of  a  continuous  increase  or  diminution  of 

1  Both  the  expressions  ''center  of  mass"  and  "center  of  gravity"  are  open  to 
objections ;  hence  certain  careful  writers  have  suggested  as  a  substitute  the  term 
centroid. 


CONSTANT  AND  ACCELERATED  VELOCITY. 

velocity,  it  is  said  to  be  accelerated.  Finally,  if  this  growth 
or  diminution  of  v.elocity  is  uniform,  it  is  said  to  have  constant 
acceleration. 

When  the  velocity  increases,  as  in  the  case  of  a  falling 
stone,  its  acceleration x  is  said  to  be  positive,  or  -}-  ;  when  the 
velocity  decreases,  as  in  the  case  of  a  stone  thrown  upward, 
its  acceleration  is  said  to  be  negative,  or  — . 

Velocity  is  determined  by  dividing  the  distance  traversed 
by  the  time  consumed.  If  a  body  move  s  feet  in  t  seconds,  its 

velocity,  v,  is  -  feet  per  second,  or  v=-.    In  case  the  velocity 

be  accelerated,  this  result  is  to  be  regarded  as  the  average 
velocity  for  that  distance  ;  and  in  the  case  of  uniform  motion 
the  average  velocity  is  the  same  as  the  actual  velocity  at  every 
instant.  It  is  evident  that  the  actual  velocity  of  a  body  whose 
motion  changes  can  be  given  only  at  some  definite  instant  or 
point  in  its  journey.  It  denotes  the  space  which  would  be 
traversed  in  a  unit  of  time,  if  at  the  given  instant  the  velocity 
should  become  constant. 

In  the  C.  G.  S.  system  the  unit  of  velocity  is  that  rate  of  dis- 
placement at  which  a  unit  of  length  is  traversed  in  a  unit  of  time, 
and  the  unit  chosen  is  a  centimeter  per  second.  Its  dimensional  is 
[L/T,  or  LT-1]. 

The  change  of  velocity  of  a  particle  per  unit  of  time  is  called 
its  rate  of  acceleration,  or  simply  its  acceleration,  and  is 
represented  by  a.  When  a  particle  acquires  equal  changes 
of  velocity  in  equal  units  of  time  its  acceleration  is  said  to  be 
constant,  and  its  motion  uniformly  accelerated.  The  accelera- 
tion of  a  body  falling  in  a  vacuum,  and  of  a  body  projected 
vertically  up  in  a  vacuum  is  practically  constant  ;  in  the 
former  case  it  is  about  32.2  feet  (or  9.8  m)  per  second,  in  the 

1  Acceleration  etymologically  means  an  increase  of  speed,  but  for  convenience 
it  has  lately  come  to  he  applied  in  scientific  treatises  to  either  an  increase  or  a 
decrease  of  speed. 


10  KIKEMATIC8. 

latter  case  it  is  a  negative  acceleration  of  about  32.2  feet 
per  second. 

The  average  acceleration,  a,  of  a  particle  in  traversing  a 
certain  distance  in  a  given  time,  and  the  rate  of  acceleration 
(also  represented  by  the  symbol  «),  provided  the  acceleration 
is  constant,  is  found  by  dividing  the  entire  change  in  velocity, 
V)  in  a  certain  time  by  the  time,  t,  taken  in  making  the  change, 

i.e.  a  =  -,  whence  v  —  a  i.     Thus,  if  the  velocity  of  a  rail- 

road train  at  a  certain  instant  be  25  miles  per  hour,  and 
half  an  hour  hence  it  be  15  miles  per  hour,  then  the  entire 
change  of  velocity,  v,  is  —  10  miles  per  hour  ;  hence  the 
average  acceleration,  i.e.  the  acceleration  if  it  were  uniformly 

distributed  throughout  the  30  minutes,  is  =  (  __  )  of  a 


mile  per  minute.     Again,  if  a  stone  falling  with  a  constantly 
accelerated  velocity  acquire  in  4  seconds  a  velocity  of  128.8  feet 

128  8 
per  second,  its  acceleration  is  —  -^—  —  32.2  feet  per  second. 

In  the  C.  G.  S.  system  the  unit  of  acceleration  is  that  acceleration 
in  which  a  unit  of  speed  is  gained  or  lost  per  unit  of  time.  Its 
dimensional  is  [LT~~2]. 


SECTION  II. 

LAWS    OF    UNIFORMLY    ACCELERATED    MOTION. 

12.  First  Law.  —  If  a  particle  be  moving  at  a  certain 
instant  at  a  rate  V,  and  its  acceleration  be  -J-  a,  then  its 
velocity,  v,  at  any  instant  is  expressed  as  follows  : 

At  the  initial  instant,  v  =  V  \ 

At  the  end  of  the  first  unit  of  time,  v  =  F+  a  X  1  ; 

At  the  end  of  two  units  of  time,  v  =  V-\-  a  X  2  ; 

At  the  end  of  t  units  of  time,  v  =  V+  a  t  (A). 

The  last,  (A),  is  a  general  equation  expressing  the  relation 


LAWS.  OF    UNIFORMLY    ACCELERATED    MOTION.         11 

between  the  velocity  (v)  at  the  end  of  any  given  unit  of 
time  (t),  the  original  velocity  (V),  and  the  acceleration  (a). 
From  this  formula  we  derive  the  following  law  : 

(1)  Change  of  velocity  due  to  uniform  deceleration  is  equal  to 
the  product  of  the  acceleration  and  the  units  of  time.  Hence  the 
change  of  velocity  is  proportional  to  the  rate  of  acceleration, 
and  to  the  time  occupied. 

13.  Second  Law.  —  If  its  initial  velocity,  V,  be  zero,  i.e.  if 
the  particle  start  from  a  state  of  rest,  the  equation  becomes 
v  =  a  t. 

Since  the  velocity  of  a  particle  starting  from  a  state  of 
rest  increases  from  zero  to  a  t,  the  average  velocity  must  be 

a    =%at.     At  this  rate  in  the  same  time,  t,   it  would 

traverse  a  distance,  S,  equal  to  ^  a  t  X  t  =  %  at'2  units  ;  hence 
S=%  a  t'2  (B).  From  this  we  derive  the  law:  (2)  The  distance 
traversed  in  a  given  time  by  a  particle  starting  from  a  state  of 
rest  and  having  uniformly  accelerated  velocity,  is  one  half  the 
product  of  the  acceleration  and  the  square  of  the  units  of  time. 
Hence  the  entire  distance  traversed  is  proportional  to  the 
square  of  the  time,  and  to  the  acceleration. 

If  a  particle,  instead  of  starting  from  a  state  of  rest,  have 
an  initial  velocity,  F,  it  would  move  in  t  units  of  time  without 
acceleration  a  distance  V  X  t ;  to  this  distance  must  be  added 
the  distance  it  moves  in  consequence  of  acceleration,  in  order 
to  obtain  the  entire  distance  traversed  in  t  units,  and  our 
formula  becomes  S  =  Vt-\-^at2  (C). 

14.  Verification.  —  The  two  laws  given  above  are  verified 
approximately  and  conveniently  by  the  use  of  the  venerable 
Atwood's  machine.1    The  equal  weights  A  and  B  (Fig.  2)  are 
suspended  by  a  thread  passing  over  the  wheel  C.     Inasmuch 
as  the  weights  are  equal  they  counterbalance  each  other  and 

1  This  machine  is  a  contrivance  which  enables  us  to  increase  the  mass  to  he  moved 
without  increasing  the  force  which  moves  it,  thus  so  decreasing  the  acceleration  as 
to  render  approximate  measurements  feasible. 


12 


KINEMATICS. 


remain  at  rest.  Raise  the  weight  A  and 
place  it  on  the  platform  D  as  shown  in  Fig.  3. 
Place  on  this  weight  a  small  additional  one, 
E,  called  a  "  rider,"  the  weight  of  which  sets 
the  system  in  motion.  Set  the  pendulum  F 
swinging.  At  each  swing  it  causes  a  stroke 
of  the  hammer  on  the  bell  G.  At  the  instant 
o|  the  first  stroke  the  pendulum  causes  the 
platform  D  to  drop  so  as  to  allow  the  weights 
to  move.  When  the  weights  reach  the  ring  H. 
the  rider,  not  being  able  to  pass  through,  is 

H  caught  off  by  the  ring.  Raise  and  lower  the 
ring  on  the  graduated  pillar  I,  and  ascertain 
by  repeated  trials  the  average  distance  the 
weights  move  between  the  first  two  strokes 
of  the  bell,  i.e.  during  one  swing  of  the 
pendulum.  Inasmuch  as  all  swings  of  the 
pendulum  are  made  in  equal  intervals  of  time, 
we  may  take  the  time  of  one  swing  as  a  unit 
of  time.  We  will  also,  for  convenience,  take 

\  for  a  unit  of  distance  the  distance  the  weights 
move  during  the  first  unit  of  time,  call  this 
unit  a  space,  and  represent  the  unit  graphically 
by  the  line  a  b  (Fig.  4). 

Next  ascertain  how  far  the  weights  move 
from  the  starting  point  during  two  units  of 
time,  i.e.  in  the  interval  of  time  between 
the  first  and  third  strokes  of  the  bell.  The 
distance  will  be  found  to  be  four  spaces, 
or  four  times  the  distance  that  they  moved 
during  the  first  unit  of  time.  This  distance 
is  represented  by  the  line  a  c. 

Now  ascertain  the  velocity  which  the 
weights  have  at  the  end  of  the  first  unit  of 


LAWS  OF  UNIFORMLY  ACCELERATED  MOTION. 


13 


time.  Place  the  ring  H  at  the 
point  (b)  which  the  weights  have 
been  found  by  trial  to  reach  at 
the  end  of  the  first  unit  of  time. 
Allow  the  weights  to  descend  as 
before.  At  the  end  of  the  first 
unit  of  time  the  rider  is  caught  off. 
At  this  instant  acceleration  ceases 
and  the  motion  becomes  uniform. 
Ascertain  how  far  the  weights  move 
with  uniform  velocity  during  the 
second  unit  of  time ;  this  velocity 
is  evidently  the  velocity  which  the 
weights  have  at  the  end  of  the  first 
unit  of  time.  This  distance  will  be 
found  to  be  (approximately  l)  two 
ci  -*, 


— .  H 


FIG.  3. 


1  U.ofT.  b-, 


2  U.of  T.  ______ 


3  U.of  T.  ._.._ 


1  space. 


Represents  the  velocity  at  the  end  of  the  first  unit 
of  time  ;  also  the  acceleration  during  the  first 
unit  of  time. 


Velocity  at  the  end  of  the  second  unit  of  time. 
Acceleration  during  the  second  unit  of  time. 


Velocity  at  the  end  of  the  third  unit  of  time. 
Acceleration  during  the  third  unit  of  time. 


4  U.ofT. ej 

FIG.  4. 

1  Approximately,  since  they  are  retarded  by  the  resistance  of  the  air  and  the 
friction  of  the  wheel. 


14  KINEMATICS. 

spaces  ;  hence  the  velocity  at  the  end  of  the  first  unit  of  time 
is  two  spaces  per  unit  of  time.  But  the  velocity  at  the  beginning 
of  the  first  unit  of  time  was  zero,  hence  the  acceleration  during 
the  first  unit  of  time  is  two.  spaces  per  unit  of  time. 

In  like  manner  determine  the  velocity  at  the  end  of  the 
second  unit  of  time.  It  will  be  found  to  be  four  spaces  per 
unit  of  time.  And  as  the  velocity  at  the  end  of  the  first  unit 
of  time  was  two  spaces  per  unit  of  time,  the  acceleration 
during  the  second  unit  of  time  is  two  spaces  per  unit  of  time. 
Hence  the  acceleration  during  the  first  two  units  of  time  is 
uniform,  and  the  change  of  velocity  during  the  first  two  units 
of  time,  as  stated  in  law  (1),  =  at  =  2  X2  =  4  spaces  per  unit 
of  time. 

Exercises. 

1.  The  velocity  of  a  particle  at  a  certain  instant  is  V ;  its  acceleration 
is  a  ;  what  will  be  its  velocity,  v,  in  t  units  of  time  afterward  ? 

2.  If  the  initial  velocity  of  a  body  be  F,  its  acceleration  a,  and  its 
final  velocity  0,  how  long,  £,  was  it  in  acquiring  its  final  velocity  ? 

3.  If  a  body  having  an  initial  velocity  V  acquire  in  t  seconds  a  velocity 
v,  what  was  its  acceleration  ? 

4.  If  a  body  move  from  a  state  of  rest  with  a  uniform  acceleration  a, 
what  space,  <S,  will  it  traverse  in  t  units  of  time  ? 

5.  If  a  body  move  from  a  state  of  rest  with  an  acceleration  a,  in  what 
time,  t,  will  it  traverse  the  space  S  ? 

6.  The  velocity  of  a  particle  at  a  certain  instant  is  20  feet  per  second  ; 
its  acceleration  is  3  feet  per  second  ;  what  will  be  its  velocity  10  seconds 
hence  ? 

7.  Suppose  that  the  acceleration  of  the  particle  mentioned  above  is 
—  2  feet  per  second,  what  will  be  its  velocity  5  seconds  after  the  instant 
named  ? 

8.  a.  A  body  falls  from  rest ;  its  velocity  increases  (if  we  disregard 
the  resistance  of  the  air)  32.2  feet  per  second.     What  is  its  velocity  at 
the  end  of  the  first  second  ?     6.  What,  at  the  end  of  the  tenth  second  ? 
c.  What,  at  the  end  of  half  a  second  ? 

9.  If  the  initial  velocity  of  a  body  be   5  feet  per  second,   its  final 
velocity  25  feet  per  second,  and  its  acceleration  2  feet  per  second,  what 
was  the  time  consumed  in  acquiring  the  final  velocity  ? 


EXERCISES.  15 

10.  A  bullet  is  projected  vertically  upward  with  an  initial  velocity  of 
161  feet  per  second ;  what  will  be  its  velocity  at  the  end  of  the  third 
second  (a  =  —  32.2  feet  per  second)  ? 

11.  How  long  will  the  bullet  named  in  the  last  problem  rise  ? 

12.  What  velocity  will  the  bullet  have  at  the  end  of  the  sixth  second, 
and  in  what  direction  will  it  be.  moving  ? 

13.  a.  What  distance  will  a  body  fall  from  a  state  of  rest  in  one 
second  ?     b.  In  two  seconds  ?     c.  In  ten  seconds  ? 

14.  A  stone  thrown  vertically  downward  is  given  an  initial  velocity  of 
40  feet  per  second.     How  far  will  it  descend  in  ten  seconds  ? 

15.  a.  A  bullet  is  projected  vertically  upward  with  an  initial  velocity 
of  225.4  feet  per  second  ;  how  long  will  it  rise  ?     6.  How  far  will  it  rise  ? 

16.  How  long  will  it  take  a  body  to  fall  1030.4  feet  from  a  state  of 
rest? 

17.  a.  A  body  falls  during  1£  seconds;  what  is  its  final  velocity? 
6.  How  far  does  it  fall  ? 

18.  A  body  falls  297.6  feet  in  4  seconds  ;  what  was  its  initial  velocity  ? 

19.  Wrhat  initial  velocity  must  be  given  a  body  that  it  may  rise  6 
seconds  ? 


16  KINEMATICS. 

SECTION   III. 

COMPOSITION    AND    RESOLUTION    OF    VELOCITIES. 

15.  Graphical  representation  of  motion  and  of  velocity.  — 
If  a  person  wish  to  describe  to  you  the  motion  of  a  ball  struck 
by  a  bat,  he  must  tell  you  three  things  :  (1)   where  it  starts, 
(2)  in  what  direction  it  moves,  and  (3)  how  far  it  goes.     These 
three  essential  elements  may  be  represented  graphically  by  a 

straight  line.     Thus,  suppose  balls 
at  A  and  D  (Fig.  5)  to  be  struck  by 

D —  — E  bats,  and  to   move   respectively  to 

B  and  E  in  one  second.    Then  the 

points  A  and  D  are  their  starting-points;  the  lines  AB  and 
D  E  represent  the  direction  of  their  motions,  and  the  lengths 
of  the  lines  represent  the  distances  traversed.  In  reading,  the 
direction  should  be  indicated  by  the  order  of  the  letters,  as 
A  B  and  D  E.  The  lengths  of  these  lines  are  not  equal  to  the 
distances  traversed  by  the  two  balls,  but  represent  these 
distances  drawn  to  some  convenient  arbitrary  scale ;  thus  on 
a  scale  of  1  cm  =  10  m,  these  lines  represent  distances  of  32 
and  20  meters  respectively. 

The  velocity  of  a  moving  body  is  described  by  giving  (1)  its 
direction,  and  (2)  the  units  of  distance  per  unit  of  time.  Since 
the  lines  AB  and  DE  represent  the  distances  traversed  by 
the  two  balls  during  the  same  unit  of  time,  these  lines  like- 
wise represent  their  average  velocities  during  this  time,  i.e.  A  B 
represents  an  average  velocity  of  32  m  per  second,  and  D  E  an 
average  velocity  of  20  m  per  second. 

16.  Composition  of  simultaneous  velocities.  —  If  a  particle 
have  by  any  means  two  or  more  separate  and  independent 
motions  communicated  to  it  simultaneously,  and  if  the  motions 
imparted  be  themselves  constant  in  velocity  and  direction,  the 
result  of  their  concurrence  is  a  single  motion  in  a  straight  line 


COMPOSITION    AND    RESOLUTION    OF    VELOCITIES.      17 

with  a  single  velocity  and  direction.  This  is  illustrated  some- 
what imperfectly  in  the  following  manner.  With  the  handle  A 
in  the  position  shown  in  Fig.  6,  push  it  forward  carrying  the 
frame  B  C  to  the  right.  This  frame  carries  a  pencil  D  whose 
point  presses  the  paper  below,  and  as  the  frame  advances,  the 
line  a  b  is  traced  upon  the  paper,  graphically  representing  the 
motion  of  the  pencil.  If,  when  the  pencil  point  is  at  a  and 
the  frame  is  at  rest,  the  string  G-  be  pulled,  the  pencil  will 
trace  the  line  ac  at  right  angles  to  ab.  Now  these  two 
independent  motions  may  be  communicated  to  the  pencil 
simultaneously  by  fastening  the  string  E  to  the  binding  screw  F 
and  pushing  forward  the  handle  A.  The  pencil  point  will  not 


FIG.  6. 

move  in  either  of  the  lines  a  b  or  a  c,  but  its  motion  will  be 
intermediate  between  the  two,  and  it  will  trace  the  line  a  d. 
This  single  motion,  which  is  the  result  of  the  concurrence  of 
two  motions,  is  called  their  resultant ;  and  they,  with  regard 
to  the  resultant,  are  called  its  components. 

The  distance  a  d  is  traversed  in  exactly  the  same  time  that 
the  distance  ab  would  be  traversed  if  the  pencil  had  no 
other  motion,  the  handle  A  being  pushed  forward  with  the 
same  speed  in  both  cases  ;  likewise  the  distance  ad  is 
traversed  in  the  same  time  that  the  distance  ac  is  accomplished, 
when  the  string  is  simply  pulled  over  the  pulley  G  with  the 
same  speed,  and  has  no  other  motion.  The  lines  ab,  ac, 
and  ad  represent  not  only  the  distances  traversed  in  the 


18 


KINEMATICS. 


several  directions,  but  also  the  magnitudes  and  directions  of 
the  respective   velocities.     For   example,   if  the   velocity   be 

constant  and  the  pencil  reach 
successively  at  the  end  of  equal 
intervals  of  time  the  points  m", 


n",  and  d  (Fig.  6a),  then  am", 
m"  n",  and  n"  d  represent  its 
velocities  in  the  successive  inter- 
vals, and  a  in,  m  n,  and  n  b  repre- 
sent the  velocities  for  the  same 
intervals  in  the  direction  a  b  ;  and  a  m',  m'  n',  and  n'  c  the 
velocities  in  the  direction  ac. 

If  points  c  and  d,  and  d  and  b  are  joined  by  (dotted)  lines, 
we  have  a  parallelogram  of  which  the  line  a  d,  representing 
the  resultant,  is  a  diagonal.  Hence  to  find  the  resultant  of 
two  simultaneous  velocities  when  they  make  an  angle  with 
each  other,  the  rule  is :  Construct  a  parallelogram  of  which 
the  adjacent  sides  represent  the  two  velocities,  and  the 
diagonal  which  lies  between  these  adjacent  sides  represents  their 
resultant. 

When  more  than  two  com- 
ponents are  given,  find  the  re- 
sultant of  any  two  of  them,  then 
of  this  resultant  and  a  third, 
and  so  on  until  every  component 
has  been  used.  For  example,  let 
the  several  velocities  imparted 
to  a  particle  be  represented  by 
the  lines  A  B,  AC,  AD,  and 
A  E  (Fig.  7).  The  resultant  of 
A  B  and  A  C  is  A  F;  the  result- 
ant of  A  F  and  A  D  is  A  G  ; 
that  of  A  G  and  A  E  is  A  H 
which  represents  the  resultant  of  the  four  velocities. 


RESOLUTION    OF    A   VELOCITY    INTO   COMPONENTS.     19 

When  two  components  are  at  right  angles  to  each  other,  it 
is  evident  that  we  may  obtain  the  magnitude  of  the  resultant 
by  finding  the  square  root  of  the  sum  of  the  squares  of  the 
two  components. 

In  case  a  particle  has  several  velocities  imparted  to  it,  all 
in  the  same  direction,  their  resultant  is  the  sum  of  all.  If 
some  are  opposite  others,  one  of  the  two  directions  is  con- 
sidered as  positive  and  the  opposite  direction  as  negative, 
and  these  signs  being  prefixed  to  the  numerical  values,  their 
algebraic  sum  is  the  resultant. 

17.  Resolution  of  a  velocity  into  components.  —  Any  motion 
or  velocity  may  be  resolved  into  two  or  any  given  number  of 
motions  of  velocities.  Let  A  B  (Fig.  8)  repre- 
sent the  velocity  and  direction  of  motion  of  a 
particle.  Draw  a  line  A  C  to  represent,  either 
arbitrarily  or  according  to  the  conditions  of 
the  problem,  one  of  the  required  components. 
Connect  B  and  (7,  draw  A  D  parallel  with  B  C,  A 
and  D  B  with  A  C,  and  thus  complete  a 
parallelogram  of  which  A  B  is  a  diagonal.  The  two  adjacent 
sides  A  C  and  AD  represent  two  component  velocities  of 
the  particle ;  in  other  words,  a  particle  having  a  velocity 
represented  by  the  line  A  B  has  at  the  same  time  velocities 
represented  in  magnitude  and  direction  by  the  lines  A  C 
and  AD. 

Exercises. 

1.  a.  If  a  ship  move  east  at  the  rate  of  10  miles  an  hour,  and  a  person 
on  deck  walk  towards  the  bow  at  the  rate  of  2  miles  an  hour,  what  is  the 
resultant  of  these  two  velocities  ?     6.  With  reference  to  what  has  he  this 
velocity  ? 

2.  Suppose  the  person  mentioned  above  walk  aft  at  the  rate  of  2  miles 
an  hour,  what  will  be  the  resultant  of  these  two  velocities  ?    b.  Prefix 
suitable  signs  to  the  numbers  given  and  represent  the  addition  which 
gives  the  resultant. 


20  KINEMATICS. 

3.  a.  A  particle  moves  simultaneously  northward  with  velocity  a,  and 
southward  with  velocity  6 ;    what  is  the  resultant  of  these  velocities  ? 
6.    How  do  you  interpret  the  resultant  if  a  >  b  ?     c.    How,  if  b  >  a  ? 
d.    How,  if  a=b? 

4.  Suppose  the  person  mentioned  above  walk  directly  north  across  the 
deck  at  the  rate  of  4  miles  an  hour,  what  will  be  the  resultant  of  these 
two  velocities  ? 

5.  Suppose  the  person  walk  northeast  at  the  rate  of  4  miles  an  hour, 
what  will  be  his  resultant  velocity  ?     [In  drawing  the  parallelogram  of 
velocities,  represent  the  component  velocities  to  some  scale,  e.g.  \  of  1 
inch  or  1  cm  =  1  mile,  then  having  completed  the  parallelogram  and 
having  drawn  the  diagonal  which  represents  the  resultant,  measure  the 
latter  and  the  result  will  express,  on  the  scale  chosen,  the  resultant 
velocity  required.] 

6.  Suppose  an  attempt  be  made  to  row  a  boat  at  the  rate  of  6  miles  an 
hour  directly  across  a  stream  flowing  at  the  rate  of  10  miles  an  hour  ; 
determine  the  direction  and  velocity  of  the  boat. 

7.  A  vessel  sails  south-southeast   (i.e.   22.5°  east  of  south)  at  the 
rate   of  14   miles  an   hour ;    determine   its  southerly   and   its  easterly 
velocity. 

8.  Represent  graphically,  to  scale,  a  velocity  of  100  feet  per  second 
and  resolve  this  velocity  into  two  components  which  shall  have  an  angle 
between  them  of  45°. 

9.  Represent  graphically  velocities,  all  in  different  directions,  which  a 
particle  has  at  a  given  instant,  as  follows :  20  feet,  30  feet,  15  feet,  and 
25  feet,  per  second.     Determine  its  apparent  velocity  and  direction. 

18.  Composition  of  constant  ivith  accelerated  velocity.  — 
Experience  teaches  that  a  body,  e.g.  a  stone,  projected  in  a 
horizontal  direction  moves  not  in  a  horizontal  path,  but  in  a 
path  intermediate  between  a  horizontal  and  a  vertical  one, 
showing  that  its  velocity  is  composed  of  a  horizontal  and  a 
vertical  component.  Its  horizontal  velocity  (if  the  resistance 
of  the  air  be  disregarded)  is  constant  and  its  vertical  velocity 
is  uniformly  accelerated.  Let  AB  (Fig.  9)  represent  the  verti- 
cal component  of  the  motion  during  the  first  second,  then  B  C 
and  C  D  will  represent  its  vertical  motion  during  the  second 
and  third  seconds  respectively.  Let  ABf,  B'C',  and  C'D'  rep- 
resent successive  horizontal  motions  during  the  same  three 


CONSTANT  WITH  ACCELERATED  VELOCITY. 


21 


periods.  Then  it  is  evident  by  a  combination  of  these  two 
motions  that  the  body  will  pass  from  A  to  B"  during  the  first 
second,  from  B"  to  C"  during  the  second  second,  and  from  C" 
to  D"  during  the  third  second.  The  body  traverses  a  curvi- 
linear path  called  a  parabola,  as  shown  in  the  figure.  In 
practice,  the  resistance  of  the  air  would  modify  the  nature 


B' 


r\L 


FIG.  9. 


of  the  curve  somewhat,  so  that  its  real  path  is  a  peculiar 
curve  known  in  the  science  of  gunnery  as  a  ballistic  curve  or 
trajectory. 

It  should  be  borne  in  mind  that  one  of  the  component 
velocities  of  a  particle  moving  in  a  curvilinear  path  is  always 
accelerated. 

Problem.  —  Imagine  a  body  to  be  projected  obliquely  upward  at  an 
angle  of  45° ;  represent  arbitrarily  its  vertically  downward  accelerated 
motion,  and  its  obliquely  upward  constant  motion  for  three  seconds, 
and  determine  the  actual  path  traversed  by  the  body  during  this 
time. 


22  KINEMATICS. 


SECTION  IV. 

KINDS    OF    MOTION. 

19.  Motion  of  translation  and  rotation.  —  In  pure  motion  of 
translation  all  the  points  of  a  body  move  with  the  same 
velocity  and  in  the  same  direction  (Fig.  10).  Example  :  the 


FIG.  10.  FIG.  11. 

Rectilinear  motion  of  translation.  Motion  of  rotation. 

motion  of  an  elevator  or  a  piston  in  the  cylinder  of  a  station- 
ary steam  engine.  When  the  points  of  a  body  describe  arcs 
of  circles  having  its  centroid  for  a  common  center,  the  motion 
is  one  of  pure  rotation  (Fig.  11).  Example  :  the  motion  of  a 
wheel  or  a  top.  All  possible  varieties  of  motion  may  be  pro- 
duced by  the  combination  of  translation  and  rotation  (Figs.  12 
and  13).  Examples  :  the  motions  of  the  planets,  that  of  a 
ball  thrown  from  the  hand,  that  of  a  carriage  wheel  along 
a  road. 

When  a  body  rotates,  every  particle  in  the  body  describes  a 
circle  around  some  point  or  line  which  is  the  center  or  axis  of 
rotation. 

The  velocity  of  a  point  far  from  the  axis  is  greater  than 
that  of  a  point  nearer  the  axis,  and,  generally,  the  velocity 
of  a  point  is  proportional  to  its  distance  from  the  axis  ; 
hence  the  expression  "  velocity  of  a  rotating  body "  is  mean- 
ingless. 


ANGULAR    VELOCITY. 


-23 


20.  Angular  velocity.  —  We  may,  however,  speak  of  the  angular 
velocity  of  the  rotating  body,  which  is  the  same  for  all  points  in  the 
body.  Angular  velocity  is  rate  of  rotation,  and  is  measured  by  the 
angle  turned  through  by  the  rotating  body  in  any  given  unit  of  time. 

The  unit  angle  in  terms  of  which  angular  velocity  is  measured  is 
called  a  radian,  and  is  the  angle  which  is  subtended  by  an  arc  equal 
in  length  to  the  radius. 

It  is  customary  then  to  express  angular  velocity  of  a  body  in 
radians  per  second,  and  this  is  numerically  equal  to  the  speed  of  a 


A 


FIG.  12. 
Translatory  and  curvilinear  motion. 


FIG.  13. 

Combination  of  translatory  and 
rotary  motion. 


point  one  unit  distant  from  the  axis.  The  Greek  letter  co  (pro- 
nounced o-meg'-a)  is  chosen  to  represent  angular  velocity. 

Now  since  the  linear  velocity  of  any  point  in  a  rotating  body  is 
proportional  to  its  distance,  r,  from  the  axis,  it  must  be  the  product 
of  the  angular  velocity  of  the  body  multiplied  by  the  distance  of  the 
point  from  the  axis,  i.e.  v=ru. 

It  remains  to  develop  a  formula  for  finding  the  value  of  w  in  terms 
of  the  time  of  a  complete  rotation.  It  is  known  that  the  ratio 
between  the  circumference  of  a  circle  and  its  diameter  is  about  3}, 
and  is  usually  represented  by  the  Greek  letter  TT.  Now  if  the 


24  KINEMATICS. 

body  make  one  rotation  in    T  seconds,  the  angular  velocity  is 
equal   to   the   total   angle,  2  IT  radians,  divided  by  the  time,    T, 

or  w  =  —  radians  per  second. 

Questions. 

1.  A  body  makes  ten  rotations  per  second;  what  is  its  angular 
velocity  ? 

2.  What  is  the  actual  velocity  of  a  point  in  this  body  ten  inches 
from  the  axis  of  rotation  ? 

3.  a.    What   is  the   angular  velocity   of   the   earth's  rotation  ? 
6.   Does  its  angular  velocity  vary  at  different  latitudes  ?     c.  Does 
the  actual  velocity  of  points  on  the  earth's  surface  vary  at  different 
latitudes  ? 

4.  What  kind  of  motion  is  that  of  the  earth  in  its  orbit  ? 

5.  Why  is  it  meaningless  to  speak  of  the  velocity  of  rotation  of  a 
body? 

6.  a.  What  motions  have  the  wheels  of  a  carriage  drawn  straight 
along  a  level  plane  ?     b.  What  motion  has  the  carriage  ? 

7.  Compare  the  several  velocities  of  the  small  front  wheels  of  the 
carriage  with  those  of  the  larger  hind  wheels. 

8.    If  a  wheel   make  200  revolutions  per   minute,   what  is  its 
angular  velocity  ? 

21.  Rectilinear  and  curvilinear  motion.  —  Besides  change  in 
velocity  or  rate  of  motion,  there  may  be  a  change  in  direction 
of  motion  (see  p.  6).  When  a  particle  moves  in  a  constant 
direction,  i.e.  in  a  straight  line,  as  in  the  case  of  a  freely  fall- 
ing bullet,  its  motion  is  said  to  be  rectilinear.  But  if  its 
motion  constantly  changes  in  direction,  i.e.  at  every  point,  as 
is  the  case  of  every  particle  in  a  rotating  wheel  except  points 
on  its  axis,  its  motion  is  said  to  be  curvilinear.  It  is 
evident  that  the  direction  of  a  motion  in  a  curvilinear  path 
can  be  given  only  for  some  specified  point,  and,  further- 
more, that  direction  can  be  represented  only  by  a  straight 
line,  for  a  curved  line  is  a  line  composed  of  an  infinite 
number  of  directions.  Let  A  (Fig.  14)  represent  a  body 
mounted  011  a  cardboard  sector  S  S'  which  is  rotated  about 


COMPOSITION    OF    CIRCULAR    MOTION. 


25 


the  axis  C  in  the  direction  indicated  by  the  arrow.  The 
body  will  move  in.  the  circular  path  ADEF.  The  straight 
line  A  B  will  indicate  the  direction  of  the  motion  at  every 
point,  but  it  will  be  seen  that  this  line  changes  its  direction 
constantly.  At  whatever  point  the  body  may  be  at  any 
instant,  the  line  A  B,  which  shows  the  direction  of  the  motion, 
is  always  tangent  to  the  curve  at  that  point. 


FIG.  14. 


FIG.  is. 


22.  Composition  of  circular  motion.  —  If  a  particle  move  in 
a  circular  path,  e.g.  a  stone  whirled  in  a  sling,  its  motion 
every  instant  is  the  resultant  of  a  tangential  motion  and  a 
centripetal  (toward  the  center)  motion.     If  when  it  passes 
point  A  (Fig.  15)  its  tangential  velocity  be  represented  by  A  B, 
its  centripetal  velocity  may  be  represented  by  B  C,  because  at 
the  end  of  the  unit  of  time  in  which  it  would  reach  B  if  it 
were  moving  in  a  straight  line,  it  is  found  to  be  not  at  B,  but 
at  some  other  point,  C,  nearer  the  center  by  the  distance  B  C. 

23.  Simple  Harmonic  Motion.  —  Besides   the   motions   of 
translation  and  rotation  already  considered,  a  third  kind  of 
motion  must  be  studied  somewhat  in  detail,  as  it  plays  so 
important  a  part  in  subjects  to  follow,  notably  sound  and 
radiation. 


26 


KINEMATICS. 


FIG.  16. 


If  a  lead  bullet  A  (Fig.  16)  be  sus- 
pended by  a  thread  and  set  swinging 
in  a  horizontal  circular  path,  the 
motion  is  practically  uniform,  and, 
when  viewed  directly  from  above  or 
below,  appears  circular.  But  if  the 
motion  of  the  bullet  be  viewed  by 
the  eye  placed  on  the  same  level 
with  it,  it  seems  to  travel  to  and  fro 
in  a  straight  line,  but  with  varying 
speed.  It  is  seen  to  move  slowly 
near  the  ends  of  its  path  and  more 
rapidly  in  the  middle.  The  motion 
of  the  bullet  as  now  viewed  is  virtu- 
ally the  projection  of  uniform  cir- 
cular motion  on  a  diameter. 

Thus,  let  Fig.  17  represent  a  particle  moving  with  uniform 
speed  in  the  circle  A  D  M  N,  as  in  the  case  of  the  swinging 
bullet.  A  line  drawn  from  this  particle  (at  the  instant  it 
passes  the  point  A  in  the 
circle)  perpendicular  to  the 
diameter  M  N,  intersects  it 
at  the  point  a.  While  the 
particle  moves  to  B,  C,  D, 
E,  F,  and  M,  this  intersect- 
ing point  moves  to  b,  c,  d, 
e,f,  and  M.  Although  the 
speed  of  the  moving  par- 
ticle is  uniform,  moving 
over  the  equal  spaces  A  B, 
BC,  CD,  etc.,  in  equal 
intervals  of  time,  the  speed 
of  the  intersecting  point  is 
variable,  moving  in  the  same  intervals  of  time  respectively 


FIG.  17. 


SIMPLE   HARMONIC   MOTION.  27 

through  the  unequal  spaces  ab,  be,  cd,  etc.  The  speed  of  this 
point  is  greatest  as  it  passes  the  center  0  of  the  circle, 
diminishes  toward  the  extremities  of  the  diameter  M  N,  and 
is  momentarily  zero  at  the  points  M  and  1ST.  Such  a  motion 
as  that,  forward  and  backward  along  the  line  MN,  executed 
in  equal  periods  of  time,  is  called  simple  harmonic  motion,  or 
S.  H.  M. 

It  is  the  kind  of  motion  executed  by  the  vibrating  prongs 
of  a  tuning  fork,  by  a  stretched  string  when  emitting  a 
musical  sound,  by  particles  of  air  when  traversed  by  sound 
waves,  and  very  nearly  by  a  pendulum  swinging  in  a  short 
arc.  A  like  motion  occurs  in  the  ether  when  traversed  by  light 
waves  or  electrical  waves,  and  in  every  elastic  medium  when 
set  in  a  tremor ;  hence  its  intimate  relation  with  many 
branches  of  physics. 

As  the  motion  repeats  itself  in  regular  intervals,  it  is  said 
to  be  periodic.  The  time  occupied  by  a  particle  in  executing 
a  single  complete  harmonic  motion,  i.e.  from  M  to  N  and 
back,  is  called  a  period.  The  period  is,  evidently,  the  time 
occupied  by  one  complete  revolution  in  the  circle  of  reference, 
as  N,  D,  M,  C',  N.  When  the  body  appears  to  move  from  left 
to  right  its  motion  is  said  to  be  positive;  and  when  from  right 
to  left,  negative.  The  extent  of  the  vibration  on  either  side 
of  its  middle  point,  as  0  M  or  0  N,  is  called  the  amplitude  of 
the  S.  H.  M.  The  distance  of  a  moving  particle  from  the  middle 
point  at  any  instant,  as  0  e,  is  called  its  displacement,  and 
points  M  and  N  are  points  of  greatest  elongation.  The  position 
of  the  particle  at  any  instant  is  denoted  by  its  phase,  which 
is  defined  as  the  fraction  of  a  period  since  the  particle  last 
passed  through  0  in  the  positive  direction. 

24.   Composition  of  Simple  Harmonic  Motions.  —  Simple  harmonic 

motions  in  the  same  or  different  directions  may  be  compounded 

according  to  the  same  laws  as  uniform  motions,  accelerations,  etc. 

We  consider  first  the  composition  of  S.  H.  M.'s  of  the  same  period. 

The  resultant  of  two  or  more  S,  H.  M.'s  of  the  same  period  and  in 


28 


KINEMATICS. 


the  same  direction  is  a  S.  H.  M.  of  the  same  period  as  that  of  the 
components  and  having  an  amplitude  equal  to  the  sum  of  the 
amplitudes  of  the  several  component  motions.  This  assumes  that 
the  phases  are  the  same.  If,  however,  a  particle  be  subjected  to 
two  S.  H.  M.'s  along  the  same  line,  but  differing  in  phase  by  half  a 
period,  the  resultant  will  be  a  motion  with  an  amplitude  equal 
to  the  difference  of  the  amplitudes  of  the  components.  That  is, 
the  particle  will  remain  at  rest  if  the  component  amplitudes 
be  equal.  • 

If  the  two  motions  be  in  the  same  phase  or  in  opposite  phases 
(i.e.  having  a  difference  of  phase  of  one-half  of  a  period)  and  at 
right  angles  to  each  other,  the  amplitude  of  the  resultant  will  be 
represented  by  the  diagonal  of  a  rectangle  constructed  upon  those 

lines  as  adjacent  sides  which  rep- 
resent the  amplitudes  of  the  com- 
ponent motions.  Thus  in  Fig.  18, 
let  A  B  and  C  D  represent  two  com- 
ponent S.  H.  M.'s  at  right  angles  to 
each  other,  the  center  of  the  circle  of 
A  reference  being  at  O.  Then  E  G  or 
F  H  will  represent  the  resultant  mo- 
tion if  the  phases  are  alike  or  oppo- 
site. 

If  the  difference  of  phase  be  only 
£  period,  then  the  resultant  motion 
will  be  a  circle,  or  an  ellipse,  accord- 
ing as  the  component  amplitudes  are  equal  or  not.  If  the  difference 
of  phase  be  a  fraction  of  a  period  not  as  simple  as  £  or  £,  then  the 
resultant  motion  in  general  will  be  an  ellipse  with  its  center  at  (), 
the  position  of  its  major  axis  depending  on  the  relation  of  the  com- 
ponent amplitudes  and  on  the  difference  of  phase. 

Experiment  1.  —  The  principles  given  above  may  be  verified 
experimentally  by  the  use  of  an  approximately  simple  pendulum. 
Partly  fill  a  small  glass  funnel  (Fig.  19)  with  fine  dark  writing  sand 
and  suspend  it  from  a  frame  above  by  means  of  a  string  (say)  1  m 
long.  It  can  be  made  to  oscillate  at  will  in  any  direction  and  the 
sand  falling  upon  a  horizontal  surface,  e.g.  a  large  sheet  of  white 
paper  or  pasteboard,  leaves  a  tracing  of  the  motions  of  the  pendulum. 
The  position  of  rest  of  the  bob  being  at  0  (Fig.  18),  give  it  an  impulse 
with  the  hand  in  the  direction  OA  sufficient  (say)  to  carry  it  to 


G 


D 
FIG.  18. 


COMPOSITION   OF    S.    H.    M'S.  29 

A.  We  may,  for  convenience,  divide  the  complete  motion  into  four 
parts,  each  of  i  period,  e.g.  from  0  to  A,  A  to  O,  O  to  B,  and  B  to 
0.  A  similar  impulse  may  be  given  to  the  bob  in  any  other  direc- 
tion, for  example  in  the  direction  0  C.  The  motions  of 
such  a  pendulum  are  approximately  S.  H.  M.'s.  The 
directions  O  A  and  0  C  will  be  considered  as  positive, 
and  their  opposites,  O  B  and  0  D,  negative. 

We  will  now  examine  four  cases :  (1)  While  the  bob  is 
oscillating  in  the  path  A  B,  gently  tap  it  with  the  hand 
in  the  direction  0  C  at  the  instant  it  passes  0  in  the  positive 
direction  ;  the  bob  will  now  move  along  the  line  0  E,  the 
diagonal  of  the  square  on  O  A  and  0  C.  In  this  case  the 
component  motions  are  in  the  same  phase,  since  both 
impulses  are  given  at  0  and  in  positive  directions. 

(2)  While  the  bob  is  moving  through  O  toward  A,  let 
the  second  impulse  be  in  the  direction  O  D ;  the  resultant 
motion  is  now  in  the  direction  0  H,  and  the  bob  oscillates 

along  the  line  FOH  without  change  of  period.     In  this    FlG>  19< 
case  the  phases  are  opposite,  differing  by  %  period. 

(3)  Let  the  impulse  be  in  the  direction  0  C,  but  applied  when  the 
bob  is  at  A  instead  of  at  0.     The  motion  now  is  in  a  circle,  the 
direction   being  anti-clockwise  (i.e.   opposite  to  the   direction   in 
which  the  hands  of  a  clock  move).     Here  the  component  B  A  is  £ 
period  ahead  of  the  component  D  C. 

(4)  If  the  impulse  be  given  at  A  in  the  direction  0  D,  the  resultant 
will  be  a  circle  still,  but  traversed  in  the  opposite  direction,  the 
component  B  A  being  now  £  period  behind  the  component  D  C. 

Observe  that  circular  motion  may  be  regarded  as  compounded  of 
two  S.  H.  M.'s  at  right  angles  to  each  other,  the  phases  differing  by 
ir  period. 

If  the  component  amplitudes  be  not  equal,  the  resultant  in  the 
case  of  the  same  or  opposite  phases  will  be  in  a  straight  line,  the 
diagonal  of  a  rectangle,  not  of  a  square.  With  the  difference  of 
phase  of  i  period,  the  circle  becomes  an  ellipse  with  its  axes  coinci- 
dent with  the  directions  of  the  component  motions. 

25.  Composition  of  S.  H.  Jf.'s  of  different  periods.  — The  motion 
resulting  from  the  composition  of  two  S.  H.  M.'s  of  different  periods 
is  more  or  less  complicated  according  to  the  ratio  of  the  periods. 
We  have  already  discussed  the  case  where  the  ratio  is  1:1.  The 
next  simpler  ratio  is  1 :2. 


30 


KINEMATICS. 


Experiment  2.  —  Suspend  from  two  tack  staples  in  a  horizontal 
bar  a  loop  of  string  (say)  2  m  long.  Slip  the  end  of  the  loop  through 
a  small  clamp  which  may  be  adjusted  at  any  height  0  (Fig.  20). 
I  — |  Adjust  so  that  0  P  =  J  C  P.  Cause  the 

'B  pendulums  0  P  and  C  P  to  oscillate  in 
planes  at  right  angles  to  each  other.  As 
C  P  is  4  0  P,  the  period  of  C  P  is  twice 
that  of  OP  (p.  78).  By  following  the 
directions  given  in  the  last  experiment, 
the  resulting  motions  may  be  observed 
and  studied.  Fig.  21  represents  the  path 
of  P  when  the  phase  differences  are  re- 
spectively 0,  £,  £  and  f  period. 

Should  the  ratio  be  not  exactly  1 : 2, 
the  different  curves  will  gradually  change 
from  one  to  another.  The  result  of  com- 
pounding S.  H.  M.'s  of  other  period  ratios 
may  be  studied  in  a  similar  manner  by 
slipping  the  clamp  up  or  down  and  thus 
changing  the  relative  lengths  of  the  two 
FIG.  20.  pendulums.  The  figures  described  on  the 

paper  by  the  falling  sand  are  exceedingly  intricate  and  interesting. 


FIG.  21. 


26.  Composition  of  S.  H.  M.  with  a  uniform  motion  at  right 
angles  to  it  ;  harmonic  curve.  —  Let  the  S.  H.  M.  of  a  particle 
be  executed  in  the  line  A  B  (Fig.  22)  ;  and  let  the  particle  at 
the  same  time  travel  with  uniform  speed  from  left  to  right. 
ACB  is  the  circle  of  reference,  which  is  divided  into  fourteen 
parts  of  equal  length  by  the  points  AC  DE,  etc.  Lines  drawn 
through  these  points  at  right  angles  to  the  line  AB  determine 
the  points  on  this  line  (viz.,  c,  d,  e,  etc.)  which  define  the 
positions  of  the  particle,  so  far  as  determined  by  the  S.  H.  M.; 


WAVE   MOTIONS. 


31 


at  equal  intervals  of  T\  of  the  period.  Lines  drawn  parallel 
to  AB  divide  the  space  into  equal  intervals,  which  represent 
the  distances  traversed  by  the  particle  from  left  to  right 
during  each  TL  of  a  S.  H.  M.  period.  Now  combining  the 
motion  AM  with  Ac,  MN  with  cd,  NP  with  de,  etc.,  we  get 
points  1,  2,  3,  etc.,  which  represent  the  actual  positions  of 
the  particle  after  successive  intervals  of  j1^  of  a  period.  If 
these  points  be  joined  by  a  gently  curving  line,  there  results 
a  characteristic  curve  called  a  Harmonic  Curve. 


A  M    N  P 


7 


FIG.  22. 

Experiment  3.  — Partly  fill  the  funnel  pendulum  (Fig.  19)  with  fine 
sand  and  suspend  it  from  a  frame.  Set  it  swinging  like  a  pendulum  bob 
and  beneath  it  move  uniformly  a  sheet  of  paper  at  right  angles  to  the 
plane  in  which  the  pendulum  swings.  The  falling  sand  will  be  deposited 
in  a  curve  which  is  approximately  a  harmonic  curve. 

The  movement  of  the  pendulum  is  approximately  S.  H.  M., 
hence  the  harmonic  curve  is  the  resultant  of  the  S.  H.  M.  of 
the  funnel  and  the  uniform  motion  of  the  strip  of  paper. 

27.  Wave  motions.  —  A,  B,  C,  D,  etc.  (Fig.  23)  represent  a 
series  of  particles  lying  in  the  same  straight  line,  e.g.  a  series 

ABCDEFG.   HI    JKLMN 


FIG.  23. 


of  particles  of  water  lying  in  the  smooth  surface  of  a  body  of 
water.  Just  below,  the  same  particles  are  represented  as 
moving  simultaneously,  each  in  a  circular  path,  in  a  vertical 


32  KINEMATICS. 

plane.  Particle  B  is  just  J.  of  a  period  behind  A,  C  the  same 
interval  behind  B,  and  so  on.  A  line  drawn  through  the  par- 
ticles in  their  several  positions  at  the  same  instant  is  called 
a  wave  line.  As  long  as  the  particles  continue  to  move  in 
their  respective  circles,  so  long  will  a  wave  form  traverse  the 
series  of  particles.  If  a  person  is  favorably  placed  so  that 
he  can  observe  a  series  of  water  waves  passing  him,  he  will 
perceive  that  floating  blocks  of  wood  move  in  elliptical  paths 
(the  circular  form  is  not  a  necessary  attribute  of  these 
motions),  never  moving  more  than  a  certain  distance  from 
certain  points  about  which  they  oscillate.  The  motions  of 
the  blocks  represent  rather  imperfectly  the  curvilinear  paths 
in  which  the  particles  composing  a  body  of  water  move  while 
that  body  is  agitated  by  waves.  To  the  observer,  ridges  and 
furrows  of  water  appear  to  move  along  the  expanse,  but 
objects  floating  upon  the  surface  are  not  carried  along  by 
them,  which  shows  that  the  appearance  is  a  deception,  and 
that  the  body  of  water  is  traversed  only  by  wave  forms. 
Observe  that,  whereas  in  Fig.  22  the  harmonic  curve  results 
in  a  combination  of  an  harmonic  and  a  uniform  translatory 
motion,  in  Fig.  23  the  wave  line  results  from  a  transmission 
of  circular  motion  to  a  series  of  particles  in  such  a  manner 
that  the  motion  of  any  particle  shall  be  a  definite  part  of  a 
period  behind  that  of  its  predecessor.  Particles  B  and  J  are 
in  positions  of  maximum  displacement  in  the  same  direction, 
and  particles  B  and  F  are  in  positions  of  maximum  displace- 
ment in  opposite  directions.  The  distance  from  B  to  J,  or 
the  distance  from  any  particle  to  the  next  particle  which  is 

J.T  i    j.-  -j_-  MPAsrEiNQ    WAVES.— The     Hon.    Ralph 

in  the  same  relative  position  11  J^^by  succeeded  m  measuring  the 

length;   the  distance  B  F  is  a  h  height  of  ocean  waves  by  Coating  a  sensiuv 

aneroid  barometer  upon  the  water.  The 
width  and  velocity  of  the  waves  were  also 
obtained  by  timing'  their  passage  with  a 
chronograph.  The  biggest  wave  he  encoun- 
tered  was  iu  5-5°  S.  latitude,  and  10  >°  \\ .  ion- 
gitude.  It  wits  4G  feet  high,  705  feet  from 
rrest  to  crest,  and  had  a  velocity  of  47  nules 
per  hour.  As  the  weather  was  not  excep 
tional  for  the  latitude,  Mr.  Abercromby  ccm- 
~i .,,!.«,  *i,nf  tvfwfis  must  occasionally  reach  a 


DYNAMICS. 


PART    I.  — CHAPTER   I. 
MOLAR    DYNAMICS. 

SECTION   I. 

FORCE.       MOMENTUM. 

28.  Dynamics  is  the  science  which  treats   of  the  action 
of  force.     This  science  will  be  treated  under  three  heads  : 
(1)  Molar  Dynamics ;   that  is,   the   dynamics   of   solids   and 
fluids,   including  the  study  of  sound  waves  ;    (2)   Molecular 
Dynamics,   including   heat  ;    (3)    Ether  Dynamics ;    that  is, 
radiation,  including  light  and  electricity. 

For  present  purposes  at  least,  we  may  regard  the  term 
Physics *  merely  as  a  generic  term  which  includes  all  these 
branches.  Hence,  Physics  is  the  science  which  treats  of  the 
dynamics  of  masses,  molecules,  and  the  ether. 

29.  Force.  —  When  a  body  at  rest  is  set  in  motion,  or  one 
which  is  in  motion  is  accelerated  (positively  or  negatively), 
or  when  a  moving  body  is  deflected  from  a  straight  course, 
experience  teaches  us  that  there  is  always  a  cause,  and  we 
have  also  learned  to  apply  to  this  cause  the  name  force.     We 
have  also  learned  that  when  a  body  is  under  the  influence  of 
a  force  which  tends  to  cause  a  change  of  motion  in  that  body, 
another  force  must  act  on  the  same  body  if  a  change  of  motion 
is  to  be  prevented. 

We  get  our  primitive  idea  of  force  from  the  sense  of 
muscular  exertion  which  we  experience  when,  by  personal 
effort,  we  put  bodies  in  motion,  or  stop  bodies  that  are  in 
motion.  We  transfer  this  conception  by  analogy  to  a  change 

1  Physics  is  often  defined  as  the  Science  of  Matter  and  Energy,  since  tf  In  the 
physical  universe  only  matter  and  energy  exist  independently  of  our  senses  and 
reason."  (Tait.) 


34  MOLAR    DYNAMICS. 

of  motion  observed  in  any  body,  and  attribute  this  change  to 
an  interaction  between  that  body  and  some  other  body,  animate 
or  inanimate.  This  interaction  is  always  a  pull  or  a,  push  and 
is  accordingly  called  an  attractive  or  a  repellent  force.  It  is 
evident  that  there  can  be  no  pull  or  push  except  between  at 
least  two  bodies  or  two  parts  of  the  same  body,  i.e.,  there  is 
no  such  thing  as  a  one-sided  pull.  In  other  words,  when 
there  is  a  pull  or  a  push  there  are  at  least  two  bodies  pulled 
or  pushed,  and  it  is  only  for  the  sake  of  convenience  in  speech 
that  we  are  permitted  to  say  that  one  body  pulls  and  the  other 
is  pulled. 

It  is  not  possible  for  a  person  to  pull  without  being  himself 
pulled,  or  to  push  without  being  himself  pushed.  Appearances 
sometimes  seem  to  contradict  the  above  statements.  For 
example,  a  man  standing  on  a  wharf  pulls  a  distant  boat  by 
means  of  a  rope.  The  boat  moves  as  the  result  of  the  pull, 
but,  though  he  is  bracing  himself  against  the  wharf,  he  is  not 
willing,  perhaps,  to  concede  that  he  is  likewise  pulled.  Let 
him  stand  in  the  boat  and  pull  the  rope  which  is  attached  at 
the  other  end  to  the  wharf  ;  both  he  and  the  boat  move. 
What  body,  according  to  appearances,  is  pulled  in  this  case  ? 
What  bodies  are  actually  pulled  ? 

We  are  now  prepared  for  a  definition  of  force.  Force  is  an 
interaction  between  two  bodies  (or  two  parts  of  the  same  body) 
causing  or  tending  to  cause  a  change  in  the  motion  of  each,  either 
in  direction  or  in  magnitude ;  or,  more  simply,  force  is  that 
which  tends  to  modify  motion. 

It  should  be  observed  that  the  above  conveys  no  idea  of 
what  the  real  nature  or  essence  of  force  is,  for  of  this  we  are 
quite  ignorant.  Indeed  we  know  of  the  existence  of  force  only 
by  its  effects ;  hence  an  idle  force,  i.e.  a  force  producing  no 
effect,  is  an  absurdity. 

30.  Force  not  a  property  of  matter.  —  We  speak  of  force  as 
exerted  by  matter,  but,  strictly  speaking,  matter  does  not  of 


ACTION    AND    REACTION.  35 

itself  exert  force.  Matter  must  be  set  in  motion  or  have  some 
form  of  energy  (see  p.  84)  conferred  upon  it  before  it  can 
exert  force,  so  that  force  is  merely  a  manifestation  of  energy. 

31.  Action  and  reaction.  —  Force  is  always  dual,  inasmuch 
as  it  is  always  oppositely  directed  upon  two  bodies.     By  a 
conventionality  of  speech  we  say  that  one  of  the  two  bodies 
acts  upon  the  other,  and  the  latter  reacts  upon  the  former. 
Later  on  it  will  be  shown  that  the  reaction  is  always  equal  to 
the  action. 

The  wings  of  a  bird  act  upon  the  air,  giving  a  certain 
portion  of  it  a  rearward  motion  ;  the  air  reacts  upon  the  wings, 
giving  the  bird  a  forward  motion.  The  bat  strikes  the  ball, 
imparting  to  it  an  acceleration,  the  ball  reacts  upon  the  bat, 
giving  it  a  negative  acceleration. 

32.  Time  required  for  bodies  to  gain  or  surrender  velocity  . — 
If  a  sled  on  which  a  child  is  sitting  be  suddenly  put  in  motion, 
the  child  is  left  in  the  place  from  which  the  sled  started.     If 
the  child  and  sled  are  both  in  motion,  and  the  sled  be  suddenly 
stopped,  the  child  lands  some  distance  ahead.     If  the  sled  be 
started  slowly,  the  child  partakes  of  the  motion  of  the  sled, 
and  is  carried  along  with  it ;  and  if  the  sled  gradually  stop, 
the  child's   motion   is   gradually  checked,   and  it  retains  its 
place  on  the  sled.     This  shows  that  masses  receive  motion 
gradually  and  surrender  it  gradually. 

Even  very  small  bodies  require  time  to  gain  or  surrender  a  definite 
velocity.  The  sand-blast,  employed  for  engraving  figures  on  glass, 
furnishes  a  fine  illustration  of  this  fact.  A  box  of  fine  quartz-sand 
is  placed  in  an  elevated  position.  A  long  tube  extends  vertically 
down  from  the  botton  of  this  box.  The  plate  of  glass  to  be  engraved 
is  covered  with  a  thin  layer  of  melted  wax.  The  design  is  sketched 
with  a  sharp-pointed  instrument  in  the  wax  when  cool,  leaving  the 
glass  exposed  only  where  the  lines  are  traced.  The  plate  is  then 
placed  beneath  the  orifice  of  the  tube,  and  exposed  to  a  shower  of 
sand.  The  velocity  of  the  sand-grains  is  not  at  its  maximum  at  the 
start,  but  is  constantly  accelerated  till  thev  reach  the  plate,  where. 


36  MOLAR    DYNAMICS. 

in  turn,  their  velocity  is  gradually  given  up.  The  wax,  on  account 
of  its  yielding  nature,  gradually  brings  them  to  rest ;  but  the  glass, 
notwithstanding  its  hardness,  cannot  stop  them  quite  at  its  surface  ; 
and,  therefore,  it  suffers  a  chipping  action  from  the  sand.  Thus  the 
soft  wax  affords  a  protection  from  the  action  of  the  falling  sand,  for 
all  parts  except  those  intended  to  be  cut.  A  still  greater  force  is 
generally  given  to  the  sand  by  steam  blown  through  the  tube.  For 
this  reason  the  apparatus  is  called  a  sand-blast.  Hard  metals  like 
steel  are  engraved  in  the  same  manner.  Yet  the  hand  may  be  held 
in  the  blast  several  seconds  without  injury. 

(Question. 

What  is  the  difference  in  the  effects  of  catching  a  base-ball  with  hands 
held  rigidly  extended,  and  with  hands  allowed  to  yield  somewhat  to  the 
motion  of  the  ball  ? 

33.  Momentum.  —  A  small  stone  dropped  upon  a  cake  of 
ice  produces  little  effect ;  a  large  stone  dropped  upon  the  ice 
crushes  it.  An  empty  car  in  motion  is  much  more  easily 
stopped  than  a  loaded  car.  Every  one  knows  that  the  effort 
to  stop  a  moving  body  depends  to  some  extent  upon  the  mass 
of  the  body.  We  have  an  instinctive  dread  of  the  approach 
of  large  masses. 

Again,  we  have  a  similar  dread  of  masses  moving  with 
great  velocities.  A  ball  tossed  is  a  different  affair  from  a  ball 
thrown.  Thus  we  are  led  to  the  consideration  of  the  mass  of 
a  body  multiplied  by  its  velocity.  This  product  is  called 
momentum.  A  large  mass,  moving  slowly,  has  great  momen- 
tum, but  the  same  mass  will  have  twice  the  momentum  if 
its  velocity  be  doubled ;  again,  a  small  mass,  moving  swiftly, 
has  great  momentum,  but  its  momentum  is  increased  in  pro- 
portion as  its  mass  is  increased.  A  unit  of  momentum  is  the 
momentum  of  a  unit  mass  moving  with  unit  speed. 

If  the  motion  of  a  mass  of  1  k,  having  a  velocity  of  1  m 
per  second,  is  taken  as  a  unit  of  momentum,  then  a  mass 
of  5  k,  moving  with  the  same  velocity,  would  have  a 


IMPULSE.  87 

momentum  of  5  ;  and  if  the  latter  mass  should  have  a  velocity 
of  10  m  per  second,  its  momentum  would  be  5  X  10  =  50. 
Hence,  the  numeric  of  momentum  is  found  by  multiplying  units 
of  mass  by  units  of  velocity ;  in  other  words,  the  product,  MV, 
of  a  mass,  M,  by  its  velocity,  F,  is  its  momentum. 

If  the  mass  and  the  velocity  both  be  unity,  the  momentum 
will  also  be  unity  ;  and  the  unit  of  momentum,  which  has 
received  no  special  name,  may  be  defined  as  the  momentum 
of  a  unit  mass  moving  with  unit  velocity,  and  momentum 
may  be  defined  as  rate  of  mass-displacement. 

The  dimensional  of  the  momentum  of  a  body  is  the  product  of  the 
dimensionals  of  its  mass  [M]  and  its  velocity  [LT-1],  i.e.  [MLT"1]. 

Since  momentum  is  a  quantity  which  has  direction, 
momentum  may  be  compounded  and  resolved  like  motions  and 
velocities. 

By  experiment,  we  learn  that  a  given  force  acting  for  two 
units  of  time  produces  twice  the  velocity  that  it  does  in  one 
unit  of  time,  and  that  the  velocity  which  a  given  force  produces 
is  proportional  to  the  time  it  acts  ;  hence  momentum,  when 
the  force  is  constant,  is  equal  to  the  product  of  the  force  and 
the  time,  i.e.  Ft ;  or  M  F—  Ft.  If  the  force  be  not  constant, 
then  the  momentum  must  be  computed  from  the  average  force 
acting.  The  product  M  V  signifies  that  the  mass-motion,  or 
momentum,  of  a  body  depends  on  its  mass  as  well  as  its  velocity. 
The  product  Ft  signifies  that  the  momentum  imparted  to  a 
body  depends  upon  the  time  (£)  during  which  a  force  acts 
as  well  as  upon  the  intensity  (F)  of  the  force.  We  infer  from 
the  above  equation  that  a  definite  force  acting  upon  any  mass 
for  a  given  time  will  generate  in  it  a  speed  whose  magnitude 
is  inversely  as  the  mass. 

34.  Impulse.  —  The  product  of  the  time  during  which  a 
force  acts  by  its  mean  intensity  is  called  the  impulse  of  the 
force.  This  term  is  usually  restricted  to  a  force  acting  for  a 


38  MOLAR   DYNAMICS. 

short  time,  as  in  a  blow  given  to  a  ball  by  a  bat.  There  is  no 
propriety  in  asking  :  "  With  what  force  does  the  bat  hit  the 
ball  ?  "  The  inquiry  may  be  with  reference  to  the  average 
pressure  which  it  exerts  on  the  ball,  or,  more  likety,  with 
reference  to  the  impulse  of  the  force,  i.e.  the  product  of 
the  mean  intensity  and  the  time  it  acts.  It  has  just  been 
shown  that  Ft  =  MV,  hence  we  infer  that  the  impulse  of  a 
force  is  measured  by  the  momentum  produced. 

Questions  and  Problems. 

1.  What  agent  is  the  immediate  cause  of  motion  ? 

2.  What  distinction  do  you  make  between  velocity  and  momentum  ? 

3.  Upon  what  does  the  momentum  given  to  a  ball  fired  from  a  gun 
by  the  expanding  gases  depend  ? 

4.  Inasmuch  as  equal  forces  are  exerted  for  the  same  length  of  time 
by  the  gases  on  the  ball  and  the  gun,  how  will  the  momenta  communicated 
to  each  compare  ? 

5.  If  there  be  25  Ibs.  of  matter  in  the  gun  and  1  oz.  (TL  lb.)  in  the  ball, 
and  the  gun  acquire  a  maximum  velocity  of  3  feet  per  second,  what,  at 
that  instant,  is  the  velocity  of  the  ball  ? 

6.  Can  any  body  be  put  in  motion  in  no  time  ?     (Demonstrate  from 
formula  Ft=  MV.) 

7.  Compare  the  momentum  of  a  car  weighing  50  tons,  moving  10  feet 
per  minute,  with  that  of  a  lump  of  ice  weighing  5  cwt. ,  at  the  end  of  the 
third  second  of  its  fall. 

8.  With  what  velocity  must  a  boy  weighing  25  K  move  to  have  the 
same  momentum  that  a  man  weighing  80  K  has  when  running  at  the  rate 
of  10  Km  per  hour  ? 

9.    Since  Ft  =  M  V,  to  what  is  change  of  momentum  proportional  ? 

10.  If  the  same  force  act  for  the  same  length  of  time  upon  bodies  hav- 
ing different  masses,  to  what  will  the  velocities  produced  be  proportional  ? 

11.  Two  boats  of  unequal  masses  are  brought  together  by  pulling  on  a 
rope.     a.  Resistance  being  disregarded,  how  will  their  momenta  at  any 
given  instant  compare  ?     6.  How  will  their  velocities  at  the  same  instants 
compare  ? 

12.  If  the  motion  of  the  moon  in  its  orbit  were  to  cease,  these  bodies 
would  approach  each  other.  The  mass  of  the  earth  is  about  80  times  that 
of  the  moon.  What  part  of  the  whole  distance  between  them  would 
the  moon  move  before  collision  ? 


FORCE    OF    GRAVITATION,    WEIGHT.  39 

35.  Force  of  gravitation,  weight.  —  It  has   been  said  that 
the   best   way    of   defining    gravitation    is   to    "let   a   stone 
drop."     In   this    phenomenon   we   discover  evidence  of   the 
action  of  a  force  between  masses ;  this  force  is  called  gravita- 
tion, or  gravity  when  the  action  is  between  the  earth  and  some 
other  mass.     Inasmuch  as  by  the  action  of  this  force  the 
earth  and  stone  are  brought  together,  this  force  has  been 
assumed  to  be,  and  is  universally  spoken  of  as,  an  attractive 
force  ;  but  the   probability  is  that  the  earth   and  stone  do 
not   draw   each   other   together,    but    are    brought    together 
through  the  agency  of  some  surrounding   medium,  and  the 
action  is  quite  as  likely  to  be  a  push  as  a  pull.     The  term 
weight  signifies  the  magnitude  of  the  force  of  gravity  which 
exists   between    any   body   and    the    earth.      It   is    usually 
determined  by  measuring  the  pressure  which  gravity  causes 
the  body  weighed  to  exert  upon  a  supporting  body,  e.g.  on  a 
scale  pan,  or  the  distortion  which  it  produces  in  the  supporting 
body,  e.g.  the  elongation  of  the  spring  in  the  spring-balance. 
The  units  generally  employed  are  the  pound  and  kilogram, 
and  are  called  the  gravitation  units  of  force.     All  forces  may 
be  measured  in  the  same  units.     To  say  that  a  man  pulls  a 
boat  with  a  force  of  one  hundred  pounds  is  equivalent  to 
saying  that  he  pulls  with  a  force  that  is  equal  to  the  force 
which  acts  between  the  earth  and  a  body  having  a  mass  of 
one  hundred  pounds.      A  force  of  one   pound,   then,   is   an 
abbreviated  expression  for  a  force  equal  to  the  weight  (at  the 
locality  in  question)  of  one  pound  of  matter. 

SECTION  II. 

MEASUREMENT    OF    FORCE. 

36.  Force  tends  to  produce  acceleration.  —  Thus  the  force  of 
gravity  causes  bodies  to  fall   with  accelerated  velocity ;    it 
also  transforms  the  otherwise  constant  velocity  of  a  body 


40  MOLAR    DYNAMICS. 

projected  upward  into  a  retarded  velocity.  A  constant  force 
acting  upon  a  free  body  (i.e.  a  body  which  encounters  no 
resistances)  always  produces  a  uniformly  accelerated  motion. 
This  is  best  illustrated  by  the  fall  or  ascent  of  a  body  in  a 
vacuum,  the  body  being  meantime  acted  on  only  by  the 
constant  force  of  gravity. 

37.  Absolute  measurement  of  force  by  direct  observation  of 
acceleration  and  mass.  —  If  a  force  F  be  applied  to  a  certain 
mass  m  for  a  unit  of  time,  a  certain  momentum  is  generated 
in  the  mass.     If  the  same  force  be  applied  to  a  greater  mass 
for  the  same  time,   it  will  move  with  as  many  times  less 
velocity  as  the^  mass  is  times  greater,  but  the  product  of  the 
mass  and  the  velocity,  i.e.  the  momentum,  is  the  same.     That 
is,  the  same  force  acting  for  the  same  length  of  time  on  free 
bodies  having  different  masses  may  be  measured  by  the  change 
of  momentum  generated  by  it  in  a  unit  of  time  (e.g.  a  second), 
since  this  is  constant  and  depends  on  nothing  but  the  force. 
That  is,  F=ma,  in  which  F  represents  any  constant  force 
acting  on  any  mass  m,  a  the  acceleration,  and  ma  the  rate  of 
change  of  momentum.    Force  is  sometimes  denned  as  the  time 
rate  of  change  of  momentum. 

38.  Absolute  units  of  force.  —  A  unit  of  force  in  the  absolute 
system  is  that  which  acting  for  a  unit  of  time  will  give  to  a 
unit  of  mass  a  unit  of  acceleration.     The  absolute  unit  of 
force  (in  the  C.  G.  S.  system)  is  called  a  dyne,  and  is  that 
force  which  in  one  second  is  capable  of  giving  to  a  gram-mass 
an  acceleration  of  one  centimeter  per  second;  in  other  words,  it 
is  a  constant  force  of  the  requisite  intensity  to  impart  in  one 
second  to  a  gram-mass  a  velocity  of  one  centimeter  per  second. 

Any  constant  force  which  in  one  second  produces  in  a  mass 
of  m  grams  an  acceleration  of  a  centimeters  per  second  must 
be  equal  to  mX  a  dynes  (i.e.  F=ma).  In  physics  the  letter  g 
is  generally  used  instead  of  the  letter  a  to  denote  the  acceler- 
ation due  to  the  force  of  gravity.  By  exact  measurement  the 


EXPRESSION    FOR    THE    MASS    OF    A    BODY.  41 

acceleration  produced  by  the  force  of  gravity  on  free  bodies 
(i.e.  in  a  vacuum)  is  found  to  be,  in  the  latitude  of  Boston  at 
the  level  of  the  sea,  980.4  cm  per  second.  Hence  the  force  of 
gravity  acting  on  a  mass  of  one  gram  must  be  (substituting, 
in  the  equation  above,  W  (weight)  for  F,  and  g  for  a) 
'  W  =  mg='LX  980.4  =  980.4  dynes.1  Consequently  it  requires 
a  force  of  980.4  dynes  to  support  (i.e.  prevent  from  falling) 
a  mass  of  one  gram  ;  or  the  weight  of  a  gram-mass  at  sea  level 
in  latitude  42°  is  980.4  dynes.  A  dyne2  is  therefore  about  ^\-$ 
of  the  weight  of  a  gram-mass,  or  exactly  7£^.7  of  the  weight  of 
a  gram-mass  at  Paris.  In  the  gravitation  system  the  weight 
of  a  gram-mass  is  a  gram-force,  hence  1  gram-force  =  980.9 
dynes  at  Paris.  Gravitation  units  in  grams-force  at  Paris  are 
readily  changed  into  dynes  by  multiplying  by  980.9  ;  at 
Boston,  by  multiplying  by  980.4  ;  and  generally  by  multiplying 
by  the  value  of  g  at  any  place. 

From  the  foregoing  statements  it  appears  that  the  weight 
of  the  gram-mass  varies  with  locality,  e.g.  Boston  or  Paris, 
so  that  the  value  of  a  gravitation  unit  of  force,  e.g.  a  gram- 
force,  is  variable.  This  want  of  definiteness  constitutes 
a  serious  objection  to  the  gravitation  system  when  great 
accuracy  is  required.  The  value  of  the  dyne  is  definite, 
absolute. 

39.    Expression  for  the  mass  of  a  body  in  terms  of  its  weight.  — 

W 

Since  W=  m  g,  m  =  -— :;  that   is,   mass    is    measured   by   its 

i/ 

weight  in  poundals 3  or  dynes,  divided  by  the  acceleration  in  feet 
or  centimeters  per  second  produced  by  gravity.     Although  W 

1  The  equation  W=.mg  expresses  the  fact  that  the  number  of  dynes  (of  gravity) 
acting  on  a  given  mass  is  g  times  the  number  of  grams-mass  in  that  body.    A  similar 
statement  holds  for  other  systems  of  units. 

2  A  dyne  is  a  very  small  force.    In  expressing  a  force  of  considerable  magnitude 
the  megadyne  (a  million  dynes)  is  commonly  used. 

3  A  poundal  is  that  force  which  in  one  second  is  capable  of  giving  to  a  pound-mass 
an  acceleration  of  one  foot  per  second. 


42  MOLAR   DYNAMICS. 

and  g  vary  with  latitude  and  elevation,  they  vary  proportion- 

W 

ally,  hence  the  ratio  —  (i.e.  the  mass)  does  not  change,  but 

y 
is  constant  for  the  same  body. 

A  body  suspended  from  a  spring  balance  (see  Fig.  24)  is  found  to  weigh 
at  Paris  i  K.  Required  its  weight  in  dynes.  Solution :  i  K  —  500  g : 
500  X  980.9  =  490,450  dynes. 

Required  to  find  the  force  which,  acting  for  10  sec.,  gave  to  a  mass  of 

10 g  a  velocity  of  1000 cm  per  sec.     Solution :  F  =  —  =  10  X  —  —  =  1000 
dynes. 

Required  to  find  the  mass  in  which  a  force  of  1500  dynes  produces  an 

F      1 500 
acceleration  of  2  cm  per  sec.     Solution:  m=—  =  ——-  =  750 g. 

Required  to  find  the  acceleration  which  a  force  of  2000  dynes  can  give 
•pi      2000 

a  mass  of  4  g.     Solution :  a  =  —  = =  500  cm  per  second. 

m        4 

40.  Measurement  of  force  by  counterbalancing.  —  The  house- 
hold instrument  called  a  spring  balance  is  strictly  speaking  a 
dynamometer,  i.e.  a  force-measurer.  It  contains  a 
spiral  spring  as  seen  in  A  (Fig.  24)  carrying  an 
index  which  moves  over  a  scale  as  shown  in  B. 
If  a  unit  of  mass  (e.g.  1  Ib.  or  1  K)  be  hung  upon 
the  spring,  it  is  lengthened  by  a  certain  definite 
quantity.  If,  grasping  the  ring  in  one  hand  and 
the  hook  in  the  other,  you  lengthen  the  spring  by 
a  muscular  pull  as  much  aS  it  was  lengthened  by 
the  force  of  gravity  acting  on  the  mass,  the  infer- 
FlGt  ^  ence  is  that  the  muscular  force  which  you  exert 
is  equal  to  the  force  of  gravity  exerted  on  the  mass,  hence  the 
spring  balance  measures  all  forces  in  gravitation  units.  A 
spring  balance  might,  however,  be  graduated  in  dynes  so  as  to 
measure  force  in  absolute  units. 

The  pound  and  the  gram  are  primarily  units  of  mass.  A 
pound-force  is  a  force  equal  to  the  weight  of  one  pound  of  matter. 


TWO    SYSTEMS    OF    MEASUREMENT    OF    FORCE.          43 

41.  Two  systems  of  measurement  of  force.  —  We  have  found 
in  the  foregoing  discussions  that  there  are  two  methods  of 
measuring  force  :  one  specially  adapted  to  measuring  balanced 
forces  (see  p.  45),  called  the  statical  or  gravitation  system  ;  the 
other  specially  adapted  to  measuring  unbalanced  forces  (see 
p.  46),  called  the  kinetic  or  absolute1  system  ;  though  a  force, 
whether  balanced  or  unbalanced,  may  always  be  measured  by 
either  system.  The  gravitation  system  is  so  called  because,  by 
it,  forces  are  compared  with  the  force  of  gravity  as  a  standard. 
The  two  methods  of  measuring  force  give  rise  to  two  systems 
of  units  called  respectively  the  gravitation  and  the  absolute 
systems,  either  one  of  which  is  easily  convertible  into  the 
other,  as  shown  above. 

Questions  and  Problems. 

1.  A  constant  force  acts  on  an  otherwise  freely  moving  body  in  a 
direction  opposite  to  that  in  which  it  is  moving ;  how  is  the  body's  motion 
affected  thereby  ?     Give  an  illustration. 

2.  How  does  a  gravitation  unit  of  force  differ  from  an  absolute  unit  ? 

3.  Would  a  spring  balance  graduated  in  grams  in  Paris  and  sensitive 
•to  the  smallest  changes  answer  for  weighing  (i.e.  determining  the  exact 

masses  of  bodies)  in  Boston  ? 

4.  What  kind  of  a  motion  does  a  constant  force  produce  on  a  free 
body  ?     How  has  this  been  shown  ? 

5.  To  what  is  the  acceleration  produced  in  equal  masses  proportional, 
i.e.  if  m  is  constant,  a  will  vary  as  what  ? 

6.  On  what  condition  will  equal  forces  produce  equal  accelerations  ? 

7.  Suppose  that  you  fill  a  box  with  sand,  place  it  on  a  toy  cart,  pull 
the  cart  by  a  string  with  a  constant  force  along  a  smooth  floor  for  a 
certain  number  of  seconds,  and  observe  the  acceleration  given  the  load 
(cart,  box,  and  sand),  then  remove  the  sand  and  replace  it  with  lead  shot; 
how  could  you  tell,  by  pulling  the  load  with  the  same  force  as  before, 
when  it  has  the  same  mass  as  the  former  load  ? 

1  Measurements  of  force  in  the  absolute  system  are  attended  with  serious  practical 
difficulties  in  the  way  of  observation  of  the  acceleration  produced,  yet  the  absolute 
units  are  almost  indispensable  in  very  many  scientific  calculations,  especially  in 
electricity  and  magnetism. 


44  MOLAR    DYNAMICS. 

8.  a.  Has  the  same  mass  equal  weights  in  Paris  and  Boston  ?   6.  How 
sensitive  must  a  spring  balance  be  to  discover  any  difference  ? 

9.  Show  that  a  spring  balance  is,  strictly  speaking,  a  force-measurer, 
and  not  a  mass-measurer. 

10.  a.  When  we  speak  of  a  force  of  one  pound,  what  do  we  mean  ? 
6.  When  we  speak  of  a  force  of  one  dyne,  what  do  we  mean  ?    c.  When 
we  speak  of  a  mass  of  one  pound,  what  do  we  mean  ? 

11.  a.  If  one  mass  is  four  times  another,  how  many  times  as  much 
force  is  necessary  to  produce  the  same  acceleration  in  the  former  as  in 
the  latter  ?     b.  How  many  times  greater  is  the  force  of  gravity  acting  on 
a  mass  of  one  hundred  pounds  than  on  a  mass  of  one  pound  ?    c.  If  a 
hundred-pound  iron  ball  and  a  one-pound  iron  ball  be  let  drop  from  the 
same  hight  at  the   same   instant,   which   ought  to  reach  the  ground 
first? 

12.  A  body  weighing  4  g  is  moving  with  an  acceleration  of  12  cm  per 
second  ;  what  is  the  force  acting  ? 

13.  A  body  acted  on  by  a  force  of  100  dynes  receives  an  acceleration 
of  20  cm  per  second  ;  what  is  its  mass  ? 

14.  A  body  of  mass  30  g  is  moved  by  a  constant  force  of  50  dynes ; 
what  is  its  acceleration  ? 

15.  What  force  acting  on  unit  mass  for  unit  time  will  cause  it  to  move 
with  unit  velocity  ? 

16.  What  acceleration  will  a  force  of  20  dynes  produce  on  a  mass 
of  10  g? 

17.  What  velocity  will  a  force  of  20  dynes  acting  on  1  K  impart  to  it 
in  5  minutes  ? 

18.  a.  What  is  the  weight  in  dynes  of  a  mass  of  1  K  in  Boston  ? 
6.  How  many  more  dynes  does  it  weigh  in  Paris  ? 

19.  A  constant  force  of  20  dynes  acts  on  a  mass  of  5  g  and  gives  it  a 
velocity  of  500  cm  per  second  ;  how  many  seconds  does  it  act  ? 

20.  How  is  the  value  in  dynes  of  a  gram  weight  at  any  locality  deter- 
mined ? 

21.  How  much  is  the  momentum  of  a  gram-mass  changed  by  gravity 
in  one  second  when  falling  freely  in  Boston  ? 

22.  Why  will  a  bullet  fired  at  an  open  door  pass  through  it  without 
moving  it  perceptibly,  while  a  push  of  the  hand,  of  much  less  intensity, 
moves  it  an  appreciable  distance  ? 

^23.    Explain  why  the  weight  of  a  body  is  not  a  perfect  measure  of  its 
mass. 

24.    What  is  the  relation  of  the  static  unit  of  force  to  the  kinetic 
unit? 


GRAPHICAL  REPRESENTATION  OF  FORCE.      45 


SECTION  III. 

COMPOSITION    AND    RESOLUTION    OF    FORCES. 

42.  Graphical  representation  of  force.  —  A  force  is  defined 
when  its  magnitude,  direction,  and  point  of  application,  are 
given.    Hence  we  may  represent  forces  graphically  by  straight 
lines  whose  lengths  bear  to  one  another  the  same  relation  as 
the  numerics  of  the  forces,  while  the  directions  of  these  lines 
indicate  the  directions  of   the  forces,  and   the  points  from 
which  the  lines  are  drawn  indicate  the  points  of  application. 
Thus,  on  a  scale  of  1  cm  =  1  k  the 

A     '    "     .....  -------  ^  -  Q 

line  A  B  (Fig.  25)  represents  a  force 

of  3.2  k  acting  toward  the  right  with    D~ 

its  point  of  application  at  A;  and 

the  line  D  E  represents  a  force  of  2  k  acting  parallel  to  the 

first  with  its  point  of  application  at  D. 

43.  Composition  of  forces  acting  in  the  same  line  ;  equilibrium 
of  forces;  balanced  and  unbalanced  forces. 


Experiment.  —  Insert  two  stout  screw-eyes  in  opposite  extremities  of 
a  block  of  wood.  Attach  a  spring  balance  to  each  eye.  Let  two  persons 
pull  on  the  spring  balances  at  the  same  time,  and  with  equal  force, 
as  shown  by  the  indexes,  but  in  opposite  directions.  —  The  block  does 
not  move.  One  force  just  neutralizes  the  other,  and  the  result,  so  far  as 
any  movement  of  the  block  is  concerned,  is  the  same  as  if  no  force  acted 
on  it. 

When  one  force  opposes  in  any  degree  another  force,  each 
is  spoken  of  as  a  resistance  to  the  other.  Let  f  represent  the 
number  of  pounds  of  any  given  force,  and  let  a  force  acting 
in  any  given  direction  be  called  positive,  and  indicated  by  the 
plus  (+)  sign,  and  a  force  when  acting  in  an  opposite  direc- 
tion to  the  force  which  we  have  denominated  positive,  be  called 
negative,  and  indicated  by  the  minus  (—  )  sign.  Then  if  two 
forces  +/  and  —  /  acting  on  a  body  at  the  same  point  or  along 


46  MOLAR    DYNAMICS. 

the  same  line  are  equal,  they  are  said  to  be  balanced,  and  the 
result  is  that  no  change  of  motion  is  produced. 

Viewed  algebraically,  -\-f — f=  0  ;  or,  correctly  interpreted, 
-{-/ — /=c=  (is  equivalent  to)  0,  i.e.  no  force.  In  all  such 
cases  there  is  said  to  be  an  equilibrium  of  forces,  and  the  body 
is  said  to  be  in  a  state  of  equilibrium. 

A  force  that  produces  equilibrium  with  one  or  more  forces 
is  called  an  equilibrant. 

If  one  of  the  forces  be  greater  than  the  other,  the  excess  is 
spoken  of  as  an  unbalanced  force,  and  its  direction  is  indicated 
by  one  or  the  other  sign,  as  the  case  may  be.  Thus,  if 
a  force  of  +  8  pounds  act  on  a  body  toward  the  east,  and 
a  force  of  — 10  pounds  act  on  the  same  body  along  the  same 
line,  then  the  unbalanced  force  is  —  2  pounds ;  i.e.  the 
result  is  the  same  as  if  a  single  force  of  2  pounds  acted  on 
the  body  toward  the  west.  Such  an  equivalent  force  is  called 
a  resultant.  A  resultant  force  is  a  single  force  that  may  be 
substituted  for  two  or  more  forces  and  produce  the  same  result 
that  the  simultaneous  action  of  the  several  forces  would  produce. 

The  resultant  of  any  number  of  forces  acting  in  the  same 
straight  line,  is  equal  to  the  algebraic  sum  of  the  forces.  An 
equilibrant  of  several  forces  is  equal  in  magnitude  to  their 
resultant,  but  opposite  in  direction.  The  process  of  combining 
several  forces  so  as  to  find  their  resultant  is  called  composition 
of  forces.  The  forces  combined  are  called  the  components. 
The  converse  operation,  of  finding  component  forces  which 
shall  have  the  same  effect  as  a  given  force,  is  called  resolution 
of  forces. 

44.    An   unbalanced  force  always  produces   acceleration.  — 
A  body  acted  on  by  an  unbalanced  force  cannot  be  at  rest. 
That  branch  of  dynamics  which  treats  of  the  relation  of  force 
to  the  motion  which  it  produces  is  called  kinetics,  and  that 
branch  which  treats  of  equilibrium  of  forces  is  called  statics. 

Equilibrium  is  often  maintained  by  the  reaction  of  a  sur- 


PRESSURE,    TENSION.  47 

face  with  which  the  body  acted  on  is  in  contact.  A  simple 
illustration  is  that  of  a  body  supported  on  a  horizontal  sur- 
face, as  of  a  table.  Here  the  reaction  caused  by  the  com- 
pression of  the  material  of  which  the  table  is  composed  is 
equal  to  the  weight  of  the  body. 

45.  Pressure,  tension.  —  A  balanced  force  does  not  produce 
acceleration,  but  causes  either  a  pressure  or  a  tension.  A  force 
exerts  pressure  when  it  tends  to  compress  or  shorten  in  the 
direction  of  its  action  the  body  on  which  it  acts.  Examples  : 
Pressure  exerted  on  the  springs  of  a  carriage,  on  air  when  it  is 
compressed  in  an  air  gun,  etc.  A  force  causes  tension  when  it 
tends  to  lengthen  in  the  direction  of  its  action  a  body  on  which 
it  acts.  A  body  thus  subjected  to  a  force  tending  to  elongate 
it  is  said  to  be  in  a  state  of  tension,  and  the  stress  to  which  it 
is  subjected  is  called  its  tension,  and  the  strength  to  resist 
being  pulled  apart  which  it  possesses  is  called  its  tensile 
strength. 

Questions  and  Exercises. 

1.  Explain  the  use  of  a  line  to  represent  force  ? 

2.  a.  When  a  force  of  100  Ibs.  is  represented  by  a  line  5  inches  long, 
what  is  the  scale  ?    b.  What  force  will  a  line  J  in.  long  represent  on  the 
same  scale  ? 

3.  a.  Represent  on  a  scale  of  J  inch  =  1  Ib.  the  resultant  of  forces  of 
5  Ibs.  and  7  Ibs.  acting  in  the  same  direction.     (Always  place  arrow 
heads  in  lines  representing  forces  to  indicate  the  direction  of  the  forces.) 
6.  Show,  by  points  A,  B,  and  C  placed  in  the  line,  the  components  of  this 
resultant,    c.  Represent  the  same  two  forces  acting  in  opposite  directions 
upon  the  same   point  A.     d.  How  will  you  represent  the  resultant  of 
these  two  opposing  forces  ? 

4.  Three  men,  A,  B,  and  C,  pull  on  a  rope  in  the  same  direction  with 
forces  respectively  of  50  Ibs. ,  60  Ibs. ,  and  70  Ibs.     A  is  nearest  the  end 
of  the  rope,  B  next,  and  C  next.     a.  What  is  the  tension  of  the  rope 
between  A  and  B  ?     6.  What,  between  B  and  C  ?     c.  A  man,  D,  just 
beyond  C  pulls  with  a  force  of  75  Ibs.  in  the  opposite  direction.     With 
what    force   must   a  man,    E,    pull,   that  there  may  be   equilibrium  ? 
d.  When  there  is  equilibrium,  what  is  the  tension  of  the  rope  between 


48  MOLAR    DYNAMICS. 

C  and  D  ?  e.  How  great  must  be  the  tensile  strength  of  the  rope 
between  C  and  D  ?  f.  Write  the  equation  showing  the  algebraic  ad- 
dition of  the  forces  in  case  of  equilibrium. 


SECTION  IV. 

COMPOSITION    OF    PARALLEL    FORCES.       MOMENTS    OF    FORCES. 

46.    Composition    of  parallel   forces    acting    in    the    same 
direction  and  in  the  same  plane. 

B  Experiment. — AB    (Fig.    26) 

represents  a  rod  lying  on  a  table 
with  three  strings  loosely  looped 
around  it  so  that  they  may  be 
slid  along  the  rod.  Dynamom- 
eters are  attached  to  the  free 
t  ends  of  the  strings.  The  strings 

»  are  all  stretched  in  parallel  direc- 

tions in  a  plane  parallel  with  the 
top  of  the  table.  (Great  care  must 

be  taken  in  the  manipulation  to  keep  the  three  strings  exactly  parallel.) 
The  dynamometers  register  the  tensions  in  the  several  strings,  i.e.  the 
forces  applied  through  them  to  the  rod. 


Observe  (I)  when  there  is  equilibrium  the-  dynamometer 
E  registers  as  much  as  those  of  F  and  G  added  together. 
(This  would  be  true  if  more  than  two  forces  were  applied  in 
the  same  direction  as  A  F  and  BG.)  But  the  force  applied  at 
C  is  the  equilibrant  of  the  other  forces  and  this  is  equal  to 
their  resultant  acting  in  the  direction  CD.  (II)  The  point 
of  application  of  the  resultant  (or  equilibrant)  is  between  the 
points  of  application  of  the  components.  (Ill)  This  point  is 
nearer  the  greater  force.  (IV)  The  distance  of  this  point 
from  the  smaller  force  is  as  many  times  greater  than  its 
distance  from  the  larger  force  as  the  larger  force  is  times  the 
smaller  force.  For  example,  if  A  F  be  14  Ibs.  and  B  G  6  Ibs., 


UNEQUAL  PARALLEL  FORCES.  49 

i.e.  14  :  6  =  7  :  3,  then  distances  C  A  and  0  B  will  be  as  3  :  7. 
In  other  words  the  component  forces  are  said  to  vary  inversely 
as,1  or  to  be  inversely  proportional  to,1  their  distances  from  their 
resultant.  These  observations  are  summarized  as  follows  : 
The  resultant  of  two  parallel  forces  in  the  same  direction  is 
equal  to  their  sum,  and  the  distances  of  their  points  of  applica- 
tion from  the  point  of  application  of  the  resultant  vary  inversely 
as  the  intensities  of  the  components. 

Corollary  :  The  condition  of  equilibrium  is  that  the  algebraic 
sum  of  the  forces  (positive  and  negative)  must  be  zero. 

When  more  than  two  forces  act  on  a  body  in  the  same 
plane  and  in  the  same  direction,  the  resultant  of  any  two  of 
them  (and  its  point  of  application)  is  found,  then  the  resultant 
of  this  resultant  and  a  third  force,  and  so  on  until  all  have 
been  used. 

47.  Composition  of  two  unequal  parallel  forces  acting  in 
opposite  directions.  —  Let  F  and  Fl  (Fig.  27)  be  parallel  forces 
acting  in  opposite  directions  on  C  B,  of  which  F  is  the  greater. 
The  force  F  may  be  resolved  into  two 
forces  :  one,  represented  by  BB1?  equal 
and  opposite  to  F!  ;  the  other  equal  to 
F  —  F15  and  represented  by  the  line  C  D. 
But  the  forces  ~F1  and  B  B!  are  in  equi- 
librium, leaving  an  unbalanced  force  at 
C  equal  to  F  —  FP  This,  then,  is  the 
resultant  R  of  the  forces  F  and  F1?  i.e. 
E  =  F—  Fi.  But  BBi:CD=AC:AB,  -  -  ^ 
and  by  composition  B  Bt  +  C  D  :  B  B!  =  ' 


AC  +  ABiACorFiF^CBiCA.  Hence  the  resultant  of  two 
unequal  parallel  forces  acting  in  opposite  directions  is  equal  to 
their  difference,  and  acts  outside  of  both  in  the  direction  of  the 

1  The  pupil  should  acquire  immediate  familiarity  with  these  expressions  of  fre- 
quent occurrence  in  physics,  and  should  practice  in  this  connection  writing  inverse 
proportions.  Thus  for  the  quantities  here  given,  14:6  =  ^:1,  i.e.  the  forces  are 
proportional  to  the  reciprocals  of  their  respective  distances  from  the  resultant. 


50  MOLAR    DYNAMICS. 

greater  component,  and  the  distances  of  its  point  of  appli- 
cation from  the  points  of  application  of  the  two  forces  are 
inversely  proportional  to  their  intensities. 

48.  Dynamical  couple.  —  If  F  and  F!  (Fig.  27)  be  equal,  the 
magnitude  of  the  resultant,  being  equal  to  the  difference  of  the 
components,  is  zero,  i.e.  they  have  no  resultant.      Two  equal 
forces  applied  to  the  same  body  in  parallel  and  opposite  directions 
not  in  the  same   line  constitute  what  is   called  a  "couple." 
The  effect  of  a  couple  is  to  produce  rotation,  but  no  motion 
of   translation.     The  value  of  a  couple  will  be  determined 
later  on. 

49.  Moment  of  a  force.  —  The  value  of  a  force  to  produce 
rotation  around  a  given  axis  is  called  its  moment  with  refer- 

A        2ft          c  3ft.  B       ence  to  that  axis.   The 

axis  is,  of   course,  al- 


20lbs-  ways   a  line    at    right 
E       angles    to    the    plane 
FlG-28-  of  rotation.      Point  C 

(Fig.  28)  may  represent  the  extremity  of  the  axis  about  which 
A  B  is  supposed  to  rotate.  The  perpendicular  distance  (C  A 
or  C  B)  from  the  axis  of  rotation  to  the  line  of  direction  in 
which  a  force  acts  (A  D  or  B  E)  is  called  the  arm  or  leverage 
of  the  force. 

The  moment  of  a  force  is  measured  by  the  product  of  the 
intensity  of  the  force  into  the 
arm.  For  example,  the  moment 
of  the  force  A  D  (Fig.  28)  '  is 
expressed  numerically  by  the 
number  (30  X  2  —  )  60,  and  the 
moment  of  B  E  is  (20  X  3  =)  60. 
By  definition  the  line  AC  (Fig.  29) 
is  the  arm  of  force  P,  and  B  C  of  the  force  Q. 

50.  Equilibrium  of  moments.  —  The  moment  of  a  force   is 
said  to  be  positive  when  it  tends  to  produce  right-hand  rota- 


j 
| 


MOMENT    OF    A    COUPLE.  51 

tion,  i.e.  in  the  direction  in  which  the  hands  of  a  clock  move, 
and  negative  when  its  tendency  is  in  the  reverse  direction. 
If  two  forces  act  at  different  points  of  a  body  which  is  free  to 
rotate  about  a  fixed  point ,  they  will  produce  equilibrium  when 
the  algebraic  sum  of  their  moments  is  zero.  Thus  the  moment 
of  the  force  applied  at  A  (Fig.  28)  is  —  (30  X  2)  =  —  60. 
The  moment  of  the  force  applied  at  B  in  an  opposite  direction 
is  accordingly  +  (20  X  3)  —  +  60.  Their  algebraic-  sum  is 
zero,  consequently  there  is  equilibrium  between  the  moments, 
and  no  tendency  to  rotation. 

When  more  than  two  forces  act  in  this  manner,  there  will 
be  equilibrium  if  the  sum  of  all  the  positive  moments  be 
equal  to  the  sum  of  all 
the  negative  moments. 

Thus,  the  sum  of  the          "1 5      D         10 

positive  moments  act-    ^1     **         ^1     a        T      ~^~        j<- 

ing  about  point  D  (Fig.      \  \  \ 

30)  is  (/)  45  +  (e)  25     1J*  8  «« 

+  (a)  30  =  100  ;      the 

sum  of  the  negative  moments  acting  about  the  same  point  is 

(c)  30  +  (d)  40  +  (b)  30  =  100  ;  the  two  sums  being  equal,  the 

moments  are  in  equilibrium. 

51.  Moment  of  a  couple.  —  The  moment  of  a  couple,  or  its 
F,    value  in  producing  rotation,  is  the  sum  of 
the  moments  of  its  two  components  around 
the  axis  of  rotation.     Let  F  and  Fx  consti- 
tute a  couple  whose  arm  is  AB  (Fig.  31). 
ITo  find  the  rotating  value  of  the  couple,  let 
P  be  the  axis  of  rotation,  then  the  moments 
F  of   F  and  Fx   relatively  to  P  are  FxAP, 

FIG-  31-  and  F!  X  B  P.     The  total  resultant  moment 

of  the  two  forces  is  (F  X  A  P)  -f  (F,.  X  B  P),  or  (since  F  =  Fx) 
FXAB. 


52  MOLAK    DYNAMICS. 


Questions  and  Problems. 

1.  Two  parallel  forces  of  8  Ibs.  and  12  Ibs.  act  in  the  same  direction 
respectively  at  points  A  and  B,  12  inches  apart.     Find  the  magnitude 
and  position  of  their  resultant. 

2.  The  smaller  of  two  parallel  forces  having  the  same  direction  is  5 
inches  from  the  resultant ;  what  is  the  distance  of  the  resultant  from  the 
other  force  ? 

3.  Two'  men  carry  a  weight  of  100  Ibs.  suspended  from  a  pole  15  feet 
long ;  each  man  is  18  inches  from  his  end  of  the  pole.     Where  must  the 
weight  be  attached  in  order  that  one  man  may  bear  f  of  it  ? 

4.  Take  from  the  last  problem  the  number  of  pounds  supported  by 
each  man  and  the  respective  distances  of  each  from  the  weight,  and  make 
an  inverse  proportion  which  shows  the  relation  that  must  exist  between 
these  quantities. 

5.  How  can  a  force  of  4  Ibs.  be  made  to  produce  equilibrium  with  a 
force  of  12  Ibs.? 

6.  Draw  a  line  2  inches  long.     Represent  on  a  scale  of  i  inch  =  1  Ib. 
a  force  of  8  Ibs.  applied  at  a  point  A  £  of  1  inch  from  one  end  of  the  line 
and  at  right  angles  to  it.     Take  for  the  axis  of  rotation  a  point  B  f  inch 
from  the  same  end  of  the  line.     From  point  C  £  inch  from  the  other  end 
of  the  line  draw  a  line  which  will  represent  a  force  that  will  produce 
equilibrium  with  the  first  force,  and  thereby  prevent  rotation. 

7.  Repeat  the  work  of  the  last  problem  except  that  the  force  applied 
at  A  shall  act  obliquely  on  the  line. 

8.  Can  a  single  force  produce  equilibrium  with  a  couple  ? 

9.  a.  A  plank  weighing  40  Ibs.   is  placed  across  a  log  so  as  to  be 
balanced.     A  boy  weighing  60  Ibs.  sits  on  one  end  of  the  plank.     Where 
shall  another  boy  weighing  90  Ibs.  sit  that  he  may  balance  the  first? 
6.  What  pressure  will  be  exerted  upon  the  log  ? 

10.  Two   horses  harnessed   abreast   are  ploughing.      How  can   you 
arrange    that  one  horse    shall    pull   only   two-thirds  as  much  as  the 
other  ? 

11.  The  maximum  muscular  force  which  a  certain  man  can  exert  is 
200  Ibs.     With  what  leverages  can  he  raise  a  stone  weighing  a  ton  ? 

12.  How  can  pressure  be  multiplied  indefinitely  ? 


CENTER    OF    MASS    DEFINED.  58 


SECTION  V. 

CENTER  OF  MASS  OR  CENTROTD. 

52.  Center  of  mass  defined.  —  Let  Fig.  32  represent  any 
body  of  matter ;  for  instance,  a  stone.  Every  particle  of  the 
body  is  acted  upon  by  the  force  of  gravitation.  The  forces  of 
gravitation  of  all  the  particles  form  a  set 
of  parallel  forces  acting  vertically  down- 
ward, the  resultant  of  which  equals  their 
sum  (§  43),  and  has  the  same  direction  as  its 
components.  The  resultant  passes  through 
a  definite  point  in  whatever  position  the 
body  may  be,  and  this  point  is  called  its 
center  of  mass,  or  centroid.  The  center 
of  mass  (c.m.)  of  a  body  is,  therefore,  the 
point  of  application  of  the  resultant  of 

all  these  forces  ;  and  for  practical  purposes  the  whole  mass  of 
the  body  may  be  supposed  to  be  concentrated  at  this  point.1  By 
the  place  or  location  of  a  body  mathematicians  mean  that 
point  where  its  center  of  mass  is  situated. 

It  is  evident  that  in  whatever  position  a  body  be  placed, 
the  resultant  of  the  weights  of  all  its  particles  passes  through  its 
centroid.  Hence,  to  support  a  body  (i.e.  to  prevent  its  falling), 
the  supporting  force,  or  equilibrant,  —  or  the  resultant  of  several 
supporting  forces,  —  must  act  in  a  line  through  the  centroid  of 
the  body  and  vertically  upward.  A  vertical  line  is  any  straight 
line  passing  through  the  centroid  of  the  earth.  Up  and  down 
are  directions  in  this  line  from  and  toward  the  earth's  centroid. 

Let  G  in  the  figure  represent  the  c.m.  of  the  stone.  For 
practical  purposes,  then,  we  may  consider  that  the  force  of 

1  The  expression  center  of  mass  does  not  necessarily  signify  that  point  occupying 
a  central  position  among  the  particles  of  a  body,  but  a  point  where,  for  convenience 
in  dynamical  problems,  we  may  consider  all  the  mass  (or  inertia)  to  be  concentrated. 


54  MOLAR   DYNAMICS. 

gravitation  acts  only  at  this  point,  and  in  the  direction  GF. 
If  the  stone  fall  freely,  this  point  cannot  deviate  from  a 
vertical  path,  however  much  other  points  of  the  body  may 
rotate  about  this  point  during  its  fall.  Inasmuch,  then,  as  the 
c.m.  of  a  falling  body  always  describes  a  definite  path,  a  line 
GF  that  represents  this  path,  or  the  path  in  which  a  body 
supported  tends  to  move,  is  called  the  line  of  direction.  It 
may  be  defined  as  a  straight  line  in  which  lie  the  centroid 
of  the  body  and  the  centroid  of  the  earth. 

To  support  any  body,  then,  it  is  only  necessary  to  provide  a 
support  for  its  centroid.  The  supporting  force  'must  be  applied 
somewhere  in  the  line  of  direction.  The  difficulty  of  poising  a 
book,  or  any  other  object,  on  the  end  of  a  finger,  consists  in 
keeping  the  support  under  its  centroid,  i.e.  in  the  line  of  direction. 

Fig.  33  represents  a  toy  called  a  "  witch,"  consisting  of  a  cylinder 
of  pith  terminating  in  a  hemisphere  of  lead.    The  toy  will  not  lie  in 
a  horizontal  position,  as  shown  in  the 
figure,   because    the    support   is   not 
applied  immediately  under  its  c.m.  at 
G;    but  when  placed  horizontally  it 
immediately  assumes  a  vertical  po- 
sition.   It  appears  to  the  observer  to 

rise ;  but,  regarded  in  a  technical  sense,  it  really  falls,  because  its 
c.m.,  where  all  the  mass  is  supposed  to  be  concentrated,  takes  a 
lower  position. 

Whether  a  body  having  no  other  support  than  that  applied  at 
its  base  will  stand  or  fall  depends  upon  whether  or  not  its  line 
of  direction  falls  within  its  base.  The  base  of  a  body  is  not 
necessarily  limited  to  that  part  of  the  under  surface  of  a  body 
that  touches  its  support.  For  example,  place  a  string  around 
the  four  legs  of  a  table  close  to  the  floor  :  the  rectangular 
figure  bounded  by  the  string  is  the  base  of  the  table.  (What  is 
the  base  of  a  man  when  standing  on  one  foot  ?  on  two  feet  ?) 

The  centroid  of  any  symmetrical  body  of  homogeneous 
material  (i.e.  of  uniform  density)  coincides  with  its  geo- 


HOW   TO   FIND   THE  CENTER   OF  MASS   OF   A  BODY.     55 

metrical  center.  Examples  :  the  middle  point  of  a  material 
straight  line  ;  that  point  on  a  straight  line  joining  the  vertex 
to  the  middle  of  the  base  of  a  triangle  situated  at  a  distance 
from  the  vertex  equal  to  two-thirds  the  length  of  the  line  ;  the 
geometrical  center  of  any  polygon,  a  sphere,  a  circular  cylinder. 

53.  How  to  find  the  center  of  mass  of  a  body.  —  Imagine 
a  string  to  be  attached  to  a  potato  by  means  of  a  tack,  as  in 
Fig.  34,  and  to  be  suspended  from 

the  hand.  When  the  potato  is  at 
rest,  there  is  an  equilibrium  of  forces, 
and  the  c.m.  must  be  somewhere  in 
the  line  of  direction  an ;  hence,  if  a 
knitting-needle  is  thrust  vertically 
through  the  potato  from  a,  so  as  to 
represent  a  continuation  of  the  verti- 
cal line  oa,  the  c.m.  must  lie  some- 
where in  the  path  an  made  by  the 

T^TP      *-& 

needle.      Suspend   the  potato  from 

some  other  point,  as  b,  and  a  needle  thrust  vertically  through 
the  potato  from  b  will  also  pass  through  the  c.m.  Since  the 
c.m.  lies  in  both  the  lines  an  and  bs,  it  must  be  at  c,  their 
point  of  intersection.  It  will  be  found  that,  from  whatever 
point  the  potato  is  supported,  the  point  c  will  always  be  verti- 
cally under  the  point  of  support.  On  the  same  principle  the 
c.m.  of  any  body  is  found.  But  the  c.m.  of  a  body  may  not  be 
coincident  with  any  particle  of  the  body;  for  example,  the 
c.m.  of  a  ring,  a  hollow  sphere,  etc. 

54.  Three  states  of  equilibrium.  —  That  a  body  acted  on 
solely  by  the  force  of  gravitation  may  be  in  equilibrium,  it  is 
necessary  and  sufficient  that  a  vertical  line  through  its  centroid 
shall  pass  through  the  point  or  surface  by  which  it  is  sup- 
ported.    The  weight  of  a  body  is  a  force  tending  downward  ; 
hence,  a  body  tends  to  assume  a  position  such  that  its  c.m.  will 
be  as  low  as  possible. 


56  MOLAR    DYNAMICS. 

Experiment.  —  Try  to  support  a  ring  on  the  end  of  a  stick,  as  at  b 
(Fig.  35).  If  you  can  keep  the  support  exactly  under  the  c.m.  of  the  ring, 
there  will  be  an  equilibrium  of  forces,  and  the  ring  will  remain  at  rest. 
But  if  it  is  slightly  disturbed,  the  equilibrium  will  be  destroyed,  and  the 
ring  will  fall.  Support  it  at  a  ;  in  this  position  its  c.m.  is  as  low  as  pos- 
sible, and  any  disturbance  will  raise  its  c.m.  ;  but,  in  consequence  of  the 
tendency  of  the  c.m.  to  get  as  low  as  possible,  it  will  quickly  fall  back  into 
its  original  position. 

A  body  is  said  to  be  in  stable  equilibrium  if  its  position  is 
such  that  any  motion  except  of  translation  would  raise  its  c.m., 
since  in  that  event  it  would  tend  to  return 
to  its  original  position.  On  the  other  hand, 
a  body  is  said  to  be  in  unstable  equilibrium 
when  a  disturbance  would  lower  its  c.m., 
since  it  would  not  tend  to  return  to  its 
original  position. 

A  body  is  said  to  be  in  neutral  or  indiffer- 
ent equilibrium  when  it  rests  equally  well 
in  any  position  in  which  it  may  be  placed. 
A  sphere  of  uniform  density,  resting  on  a  horizontal  plane, 
is  in  neutral  equilibrium,  because  its  c.m.  is  neither  raised  nor 
lowered  by  a  change  of  base.  Likewise,  when  the  support  is 
applied  at  the  c.m.,  as  when  a  wheel  is  supported  by  an  axle, 
the  body  is  in  neutral  equilibrium. 

It  is  evident  that  if  the  c.m.  be  below  the  support,  as  in  the 
last  experiment  with  the  ring,  the  equilibrium  must  be  stable : 
but  a  body  may  be  in  stable  equilibrium,  though  its 
c.m.  be  above  the  point  of  support.  (When  is  this 
possible  ?) 

It  is  difficult  to  balance  a  lead-pencil  on  the  end  of 
a  finger ;  but  by  attaching  two  knives  to  it,  as  in  Fig. 
36,  the  c.m.  may  be  brought  below  the  support,  and 
it  may  then  be  rocked  to  and  fro  without  falling.  Fl()-  3t)- 

55.  Stability  of  Bodies.  —  The  ease  or  difficulty  with  which 
bodies  supported  at  their  bases  are  overturned  varies  with  the 


STABILITY    OF    BODIES. 


57 


liight  to  which  their  c.m.  must  be  raised  to  overturn  them. 
The  letter  c  (Fig.  37)  marks  the  position  of  the  c.m.  of  each  of 
the  four  bodies  A,  B,  C,  and  D.  If  any  one  of  these  bodies 
be  overturned,  its  c.m.  must  have  passed  through  the  arc  ci, 
and  have  been  raised  through  the  hight  ai.  By  comparing  A 
with  B,  and  supposing  them  to  be  of  equal  weight,  we  learn 
that  of  two  bodies  of  equal  weight  and  hight  of  c.m.,  the  c.m.  of 
that  body  which  has  the  larger  base  must  be  raised  higher,  and 
that  body  is,  therefore,  overturned  with  greater  difficulty.  A 


i 

ma 


B  C  D 

FIG.  37. 

comparison  of  A  and  C,  supposing  them  to  be  of  equal  weight, 
shows  that  when  two  bodies  have  equal  bases  and  weights,  the 
body  having  its  c.m.  higher  is  more  easily  overturned.  D  and  C 
have  equal  masses,  bases,  and  bights,  but  D  is  made  heavy  at 
the  bottom,  and  this  lowers  its  c.m.  and  gives  it  greater  stability. 


Questions  and  Exercises. 

1.  Where  is  the  centroid  of  a  box  ? 

2.  Why  is  a  pyramid  a  very  stable  structure  ? 

3.  What  is  the  object  of  ballast  in  a  vessel  ? 

4.  State  several  ways  of  giving  stability  to  an  inkstand. 

5.  a.  Tn  what  position  would  you  place  a  cone  on  a  horizontal  plane, 
that  it  may  be  in  stable  equilibrium  ?     b.  That  it  may  be  in  neutral 
equilibrium  ?     c.  That  it  may  be  in  unstable  equilibrium  ? 

6.  In  loading  a  wagon,  where  should  the  heavy  luggage  be  placed  ? 
Why? 


58 


MOLAR    DYNAMICS. 


7.  Why  are  bipeds  slower  in  learning  to  walk  than  quadrupeds  ? 

8.  Why  is  mercury  placed  in  the  bulb  of  a  hydrometer  ? 

9.  How  will  a  man   rising  in  a 
boat  affect  its  stability  ? 

10.  Which  is  more   liable   to  be 
overturned,  a  load  of  hay  or  a  load 
of  stone  of  equal  weight  ? 

11.  Draw  a  triangle  and  find  its 
center  of  mass. 

12.  What   attitude    does  a  man 
assume  when  carrying  a  heavy  load 
on  his  back  ?     Why  ? 

13.  Explain  the  difference  in  the 
behavior  of  a  ball   and   of  a  cube, 
when  placed  on  a  plane  slightly  in- 
clined. 

14.  What  position  do  bodies  floating  in  air  or  in  water  take  ? 

15.  a.  Explain  how  the  toy  horse  (Fig.  38)  stands  upon  the  platform 
without  falling  off.      6.  Explain  how  the  toy  may  rock  upon  its  support 
without  falling  off. 

i  SECTION  VI. 


COMPOSITION    OF    FORCES    ACTING    AT    ANGLES    WITH    ONE 
ANOTHER. 

56. .  When  the  handle  A  (Fig.  6)  is  pushed  forward,  there 
is  applied  to  the  pencil  a  force  which  may  be  represented  in 
magnitude  and  direction  by  the  line  a  b  \  at  the  same  time 
the  pencil  is  pulled  vertically  up  by  a  force  which  may 
properly  be  represented  by  the  line  a  c.  The  pencil,  however, 
moves  in  the  line  a  d,  which  is  a  diagonal  of  a  parallelogram 
constructed  on  the  lines  a  b  and  a  c.  It  is  evident  that  a  single 
force  might  be  applied  to  the  pencil  with  the  same  effect  that 
the  two  forces  produce.  Obviously,  if  a  single  force  were  to 
move  the  pencil  in  the  line  a  d,  it  must  have  the  direction  of 
this  line.  It  remains  to  ascertain  whether  the  diagonal  line 
a  d  represents  the  magnitude  of  the  resultant.  Evidently  if 


COMPOSITION   OF    FORCES. 


59 


this  diagonal  does  represent  the  resultant,  then  the  same 
diagonal  with  the  direction  reversed  will  'represent  the 
equilibrant  of  these  forces.  We  put  the  matter  to  an  experi- 
mental test  with  other  apparatus  : 

Experiment.  —  Insert  pegs  in  any  three  holes  of  the  circle  in  the  top 
of  the  circular  table,  Fig.  39.     Join  these  by  threads  attached  to  a  spring 


FIG.  39. 

balance  as  shown  in  the  figure.  Stretch  the  balances  so  as  to  indicate 
any  desired  pull  in  each  of  the  threads.  Place  under  the  threads  a  sheet 
of  white  paper.  Locate  on  the  paper  the  common  point  of  application  A 
of  the  three  forces.  Draw  lines  A B,  AC,  and  A D,  to  represent  the 
directions  in  which  the  forces  act.  Since  the  point  A  does  not  move,  it 
is  evident  that  the  three  forces  are  in  equilibrium  and  that  any  one  of  the 
three  forces  is  the  equilibrant  of  the  other  two.  Select  any  one  for  an 
equilibrant  (e.g.  AD)  and  extend  it  in  an  opposite  direction  from  A, 


60 


MOLAR    DYNAMICS. 


representing  (on  some  suitable  scale)  a  force  A  E  equal  to  and  opposite  to 
the  force  A  D  as  indicated  by  the  dynamometer  D.  On  the  same  scale 
lay  off  distances  A  B  and  A  C  representing  the  magnitudes  of  the  forces 
acting  in  the  directions  of  these  lines.  The  line  AE  is  by  definition 
(§  43)  the  resultant  of  A  B  and  A  C.  Connect  E  with  C  and  B.  The 
figure,  if  the  work  be  done  with  care,  will  be  found  to  be  a  parallelogram. 
The  diagonal  EA  represents  the  magnitude  of  the  equilibrant  of  the 
forces  A  B  and  AC,  and  the  same  line  with  the  direction  reversed  (i.e. 
A  E)  represents  the  resultant. 

57.  Parallelogram  of  forces.  —  If  two  forces  applied  at  a 
point  be  represented  in  magnitude  and  direction  by  the  adjacent 
sides  of  a  parallelogram,  their  resultant  will  be  represented  in 
magnitude  and  direction  by  the  diagonal  which  passes  through 
that  point. 

This  proposition  is  applicable  whether  the  forces  act  on  a 
particle  or  on  a  rigid  body  provided  they  lie  in  the  same  plane. 


Thus,  let  two  forces  applied  at  points  A  and  B  of  a  stone 
(Fig.  40)  act  in  the  directions  A  C  and  B  D  respectively. 
The  direction  of  the  resultant  must  pass  through  E,  the  point 
where  the  lines  of  direction  of  the  given  forces  produced  back- 


COMPOSITION    OF    FORCES. 


61 


wards  intersect.  If,  now,  the  lines  EC  and  E  D  be  laid  off  to 
represent  the  relative  intensities  of  the  forces,  the  diagonal 
E  F  of  the  parallelogram  constructed  thereon  will  represent 
their  resultant,  and  its  point  of  application  may  be  G  or  any 
other  point  in  the  line  G  H. 

58.  Composition  of  wore  than  two  forces  in  the  same  plane. — 
When  more  than  two  components  are  given,  find  the  resultant 
of  any  two  of  them,  then  of  this  resultant  and  a  third,  and  so  on 
till  every  component  has  been  used.  Thus,  in  Fig.  41,  A  C  is 
the  resultant  of  A  B  and  A  D,  and 
A  F  is  the  resultant  of  A  C  and  A  E, 
i.e.  of  the  three  forces  A  B,  AD, 
and  A  E.  (Invent  several  problems 
similar  to  this,  in  which  three,  four 
or  more  forces  are  to  be  combined, 
and  work  out  the  results.) 

Generally  speaking,  a  motion 
may  be  the  result  of  any  number  of  forces.  When  we  see  a 
body  in  motion,  we  cannot  determine  by  its  behavior  how 
many  forces  have  concurred  to  produce  its  motion. 

59.  Triangle  of  forces.  —Since  in  Fig.  39  BE  =  AC,  the  three 
forces  which  are  represented  in  the  parallelogram  by  the  lines  A  B 
A  C,  and  A  E,  are  also  represented  by  A  B,  B  E,  and  A  E,  three 
sides  of  a  triangle  ABE. 

Hence,  if  two  forces  are  represented  by  two  sides  of  a  triangle,  the 
third  side  will  represent  their  resultant. 

60.  Polygon    of  forces.  —  //  any 
number  of  forces  applied  at  a  point 
are  represented  by  all  the  sides  but  one 
of  a  polygon,  the  remaining  side  will 
represent  their  resultant.      Thus  the 
forces  AB,  AD,  and  AE  (Fig.  41)~ 
are   represented   respectively   by   the 
sides  A' B',  B' C'  (=  A  D),  and  C'F' 
(  =  A  E)    of    a   polygon   A'  B'  C'  F' 

(Fig.  42),  that  is  completed  by  the  side  A'F'  (=  A  F),  which  rep- 
resents the  resultant  of  the  three  forces. 


FIG.  42. 


62 


MOLAR    DYNAMICS. 


61.    Parallelepiped  of  forces.  —  //  three  forces  not  in  the  same 

plane  are  applied  at  a  point,  they 
will  form  three  edges  of  a  paral- 
lelopiped,  and  that  diagonal  of 
this  solid  which  is  concurrent  with 
these  edges  will  represent  the  re- 
sultant of  these  forces.  It  will  be 
readily  seen  that  the  resultant  of 
the  forces  A  B,  AD,  and  A  C 


FIG.  43. 


FIG.  44. 


(Fig.  43),  is  represented  by  the  diagonal  AE. 

62.  Resolution  of  forces.  —  Assume  that  a  ball  has  an 
acceleration  in  a  certain  direction  A  C  (Fig.  44),  and  that  one 
of  the  forces  that  produces  this  acceleration  is  represented  in 
intensity  and  direction  by  the  line  A  B ;  what  must  be  the 
intensity  and  direction  of  the  other  force  ?  Since  A  C  is  the 
resultant  of  two  forces  acting  at  an  angle  to  each  other  it  is 
the  diagonal  of  a  parallelo- 
gram of  which  AB  is  one 
of  the  sides.  From  C,  draw 
CD  parallel  and  equal  to 
B  A,  and  complete  the  paral- 
lelogram by  connecting  the 
points  B  and  C,  and  A  and  D.  Then,  according  to  the 
principle  of  composition  of  forces,  A  D  represents  the  inten- 
sity and  direction  of  the  force  which,  combined  with  the  force 
A  B,  would  move  the  ball  from  A  to  C.  The  component  A  B 
being  given,  no  other  single  force  than  A  D  will  satisfy  the 
question. 

Had  the  question  been,  What  forces  can  produce  the  motion 
AC?  an  infinite  number  of  answers  might  be  given.  In  a 
like  manner,  if  the  question  were,  What  numbers  added 
together  will  produce  50  ?  the  answer  might  be  20  +  30, 
40  +  10,  20  -f-  20  -f- 10,  and  so  on,  ad  infinitum  ;  but  if  the 
question  were,  What  number  added  to  30  will  produce  50  ? 
only  one  answer  could  be  given. 


BESOLUTION    OF   FORCES. 


63 


It  is  often  necessary  to  resolve  a  force  in  order  to  ascertain  the 
effective  force  in  a  certain  direction.  Thus  when  boat  sails  are 
exposed  obliquely  to  the  wind,  the  pressure  effectual  in  moving  the 
boat  is  only  a  component  of  the  whole  force  of  the  wind.  The  line 
af  (Fig.  45)  represents  the  force  of  the  wind  acting  on  the  sail  c  d  at 
the  point  a.  Resolving  this  force  we  obtain  the  components  2 


(normal  to  the  sail)  and  1  (a  useless  component  called  a  tail  wind). 
The  boat  does  not  move  in  the  direction  of  the  pressure  on  its  sail, 
because  it  is  more  easily  moved  lengthwise  than  breadthwise.  Hence 
the  normal  pressure  must  be  resolved  into  two  components,  one  4 
along  the  direction  of  least  resistance,  i.e.  the  direction  of  easy 
motion,  the  other  3  at  right  angles  to  it.  The  latter  component 
does  tend  to  cause  a  slow  broad-side  motion  called  leeway,  but  this 
may  be  partly  counteracted  by  a  deep  keel  or  a  center-board  so  that 
the  boat  will  sail  approximately  along  the  line  a  b. 

Problems. 

1.   Draw  upon  paper  pairs  of  lines  making  about  the  same  angles  with 
each  other  as  A  B  and  A  C  in  the  four  diagrams,  Fig.  46,  and  having 


B    B 


about  the  same  directions ;  assign  arbitrarily  numerical  values  to  each 
component,  drawing  to  scale,  and  find  the  direction  and  the  numerical 
value  of  the  resultant  of  each  pair  of  components. 


64  MOLAR    DYNAMICS. 

2.  a.  Find  the  intensity  of  the  resultant  of  two  forces  acting  at  an 
angle  of  45°.    b.  Find  the  intensity  of  their  resultant  when  they  act  at  an 
angle  of  150°.     (The  pupil  will  require  either  a  pair  of  dividers  or  a  pro- 
tractor.    He  will  do  well  to  learn  to  use  both  in  measuring  angles.) 

3.  a.  A  heavy  rock  rests  upon  a  smooth  plane ;  two  men,  A  and  B, 
pull  the  rock  by  means  of  ropes  attached  to  it,  A  with  a  force  of  100  Ibs., 
B  with  a  force  of  150  Ibs.     If  A  pull  toward  the  north  and  B  toward  the 
south,  what  will  be  the  resultant  ?     b.  If  A  pull  toward  the  east  and  B 
toward  the  south,  what  will  be  the  resultant  ?     c.  In  the  last  case,  if  the 
easterly  acceleration  at  a  certain  instant  is  10  feet  per  minute,  what  is 
the  southerly  acceleration  at  the  same  instant?     d.  In  what  direction 
should  they  pull  the  rock  to  give  it  the  maximum  acceleration  ?     e.  If  A 
pull  it  25°  S.  of  E.,  in  what  direction  and  with  what  force  may  B  pull  it 
that  the  resultant  may  be  directly  east  ?    /.  Give  a  different  answer  to 
the  last  question. 

4.  On  a  scale  of  1  cm  =  1  K,  represent  a  force  of  5  K  acting  north- 
ward on  a  point  A. 

5.  On  a  scale  of  1  cm  =  1  K,  represent  forces  of  4  K,  6  K,  and  8  K, 
acting  simultaneously  on  point  A  in  directions  respectively  as  follows : 
N.,  N.  E.,  and  S.  E.     Find  their  equilibrant. 

6.  A  ship  is  sailing  N.  N.  E.  at  the  rate  of  12  knots  per  hour.     Find 
its  northerly  and  easterly  velocities. 

7.  Find,  both  by  construction  (of  parallelogram)  and  by  calculation, 
the  intensity  of  two  equal  forces  acting  at  right  angles  to  each  other,  that 
will  support  a  weight  of  15  pounds. 

8.  A  sailor  climbs  a  mast  at  a  uniform  rate  of  5  feet  a  minute  while 
the  vessel  moves  forward  at  the  rate  of  15  feet  a  minute  ;  what  is  his 
actual  velocity  ? 

9.  On  a  scale  of  £  of  one  inch  =  10  Ibs.,  represent  a  force  of  80  Ibs. 
Resolve  this  force  into  two  forces  one  of  which  shall  act  at  an  angle  of 
30°  with  the  given  force.     Determine  the  numerical  intensities  of  each  of 
the  components. 

10.  Show  by  construction  that  a  north-east  wind  is  made  up  of  a 

north  and  an  east  wind,  each  — —  of  the  actual  velocity  of  the  wind. 

vi 

11.  If  two  lines  AB,  C  A  Represent  two  forces  acting  on  point  A,  the 
one  toward  and  the  other  from  it,  show  how  to  find  the  resultant. 

12.  Find  the  resultant  of  two  equal  forces  of  P  Ibs.,  the  angle  between 
them  being  120°. 

13.  Two  rafters,  making  an  angle  of  60°,  support  a  chandelier  weighing 
90  Ibs. ;  what  is  the  pressure  along  each  rafter  ?     Ans.  51.96  pounds. 


LAWS    OF    MOTION.  65 


SECTION    VII. 
DISCUSSION  OF  NEWTON'S  THREE  LAWS  OF  MOTION. 

03.  Laws  of  motion.  —  The  science  of  dynamics  rests  on 
certain  fundamental  principles  termed  the  Laws  of  Motion, 
first  clearly  stated  by  Newton  in  the  "Principia"  two  cen- 
turies ago,  and  verified  by  universal  experience.  The  laws  as 
given  in  this  text-book  are  as  originally  enunciated  by  New- 
ton, with  very  slight  verbal  modifications  in  conformity  to 
modern  terminology. 

First  Law :  A  body  at  rest  remains  at  rest,  and  a  body  in 
/not in/i  continues  to  move  ivith  constant  speed  in  a  straight  line, 
unless  acted  upon  by  some  external  unbalanced  force. 

This  law  may  be  paraphrased  as  follows  :  A  body  under  the 
action  of  no  force,  or  of  balanced  forces,  is  either  at  rest  or  in 
uniform  motion  ;  if  it  be  at  rest  it  will  remain  at  rest,  and  if 
it  be  in  motion,  its  motion  will  be  in  none  other  than  a  straight 
line,  and  its  velocity  will  never  change. 

Motion  unobstructed  is  perpetual.  "  Is  perpetual  motion 
possible  ?  "  has  been  often  asked.  The  answer  is  simple,  — 
yes,  more  than  possible,  often  necessary,  if  no  force  interfere  to 
prevent.  (Example  :  the  motions  of  the  planets.)  On  our 
earth  we  have  no  instances,  for  resistances  such  as  friction, 
resistance  of  the  air,  etc.,  are  continually  opposed  to  all 
movements  of  terrestrial  bodies.  On  this  account  we  find 
that  force  is  required  to  perpetuate  the  motion  of  all  bodies 
with  which  we  deal,  and  we  fall  readily  into  the  fallacy  that 
force  is  necessary  to  maintain  motion,  which  the  First  Law 
distinctly  contradicts. 

The  clause  "  Unless  acted  upon  by  an  external  force  "  virtu- 
ally states  that  "All  matter  is  inert,"  i.e.  that  bodies  of  mat- 
ter are  utterly  incapable  of  putting  themselves  in  motion  or 
stopping  themselves  ;  the  inability  is  called  inertia.  Inertia 


66  MOLAR    DYNAMICS. 

may  be  defined  as  that  property  of  matter  in  virtue  of  which 
external  force  is  required  to  produce  a  change  in  momentum. 
It  is  the  sole  unalterable  property  of  matter. 

The  terms  mass  and  inertia  are  often  used  interchangeably  to 
denote  a  quantity  proportional  to  the  unbalanced  force  required 
to  produce  a  given  change  in  the  velocity  of  a  body  in  a  given 
time.  It  is  known  that  all  bodies  unobstructed  by  the  air  fall 
with  the  same  velocity  irrespective  of  their  masses  or  inertia.  But 
to  produce  equal  acceleration  in  equal  times  requires  forces  propor- 
tional to  the  masses ;  it  follows,  then,  that  at  the  same  locality 
weight  and  mass  (or  inertia)  are  proportional.  Hence  we  compare 
masses  by  comparing  their  weights. 

The  somewhat  vague  yet  common  expressions  "to  overcome 
inertia"  and  "to  destroy  inertia"  mean  to  produce  a  certain 
change  of  mass-motion  (i.e.  momentum),  and  may  signify  either  an 
increase  or  a  decrease  of  the  same. 

/Second  Law :  Change  of  momentum  is  in  the  direction  in 
which  the  unbalanced  force  acts,  and  is  proportional  to  its  inten- 
sity and  to  the  time  during  which  it  acts. 

It  will  be  seen  that  this  law  (except  as  regards  direction) 
is  contained  in  the  formula  MV=Ft  (p.  37)  which  has 
already  been  developed.  This  formula  virtually  asserts  that 
where  there  is  no  force  there  is  no  change  of  momentum 
(i.e.  if  F  =  Q,  Ft  =  0).  Hence  the  First  Law  of  Motion  is  a 
deduction  from  the  Second. 

This  law  declares,  by  implication,  (1)  that  an  unbalanced 
force  in  a  given  time  always  produces  exactly  the  same  change 
of  momentum  regardless  of  the  mass  of  the  body /  that  an 
unbalanced  force  never  fails  to  produce  a-  change  of  momentum, 
hence  any  force,  however  small,  can  move  any  body  of  however 
great  mass.  For  example,  a  child  can  move  a  body  having  a 
mass  equal  to  that  of  the  earth,  provided  only  that  the  motion 
of  this  body  is  not  hindered  by  a  third  body.  Moreover,  the 
quantity  of  momentum  that  the  child  can  generate  in  this 
immense  body  in  a  given  time  is  precisely  the  same  as  that 


LAWS   OF   MOTION.  67 

which  he  would  generate  by  the  exertion  of  the  same  force  for 
the  same  length  of  time  on  a  body  having  a  mass  of  (say)  10 
pounds.  Momentum  is  the  product  of  mass  into  velocity; 
so,  of  course,  as  the  mass  is  large,  the  velocity  acquired  in  a 
given  time  will  be  correspondingly  small.  The  instant  the 
child  begins  to  act,  the  immense  body  begins  to  move.  Its 
velocity,  infinitesimally  small  at  the  beginning,  would  increase 
at  an  almost  infinitesimally  slow  rate,  so  that  it  might  be 
years  before  its  motion  would  become  perceptible. 

It  is  easy  to  see  how  persons  may  get  the  impression  that 
very  large  masses  are  immovable  except  by  very  great  forces. 
The  erroneous  idea  is  acquired  that  bodies  of  matter  are  capa- 
ble of  resisting  the  tendency  of  forces  to  cause  motion,  and 
that  the  greater  the  mass,  the  greater  the  resistance  ("  quality 
of  not  yielding  to  force,"  Webster).  The  fact  is,  that  no  body 
of  whatever  'mass  can  resist  motion  ;  in  other  words,  "  a  body 
free  to  move  cannot  remain  at  rest  under  the  slightest  unbalanced 
force"  But  as  time  is  always  required  to  generate  change  of 
momentum,  there  arises  thence  a  deceptive  appearance  of 
resistance  or  holding  back. 

This  law  declares  by  implication,  (2)  that  a  force  acting 
on  a  body  in  motion  produces  just  the  same  effect  as  if  it  were 
acting  on  the  same  body  at  rest,  for  no  reference  is  made  in  the 
law  to  the  state  of  the  body  acted  upon. 

Experiment.  —  Draw  back  the  rod  d  (Fig.  47)  towards  the  left,  and 
place  the  detent-pin  c  in  one  of  the  slots.  Place  one  of  the  brass  balls  on 
the  projecting  rod,  and  in  contact  with  the  end  of  the  instrument,  as  at  A. 
Place  the  other  ball  in  the  short  tube  B.  Raise  the  apparatus  to  as  great 
an  elevation  as  practicable,  and  place  it  in  a  perfectly  horizontal  position. 
Release  the  detent,  and  the  rod,  propelled  by  the  elastic  force  of  the 
spring  within,  will  strike  the  ball  B,  projecting  it  in  a  horizontal  direc- 
tion. At  the  same  instant  that  B  leaves  the  tube  and  is  free  to  fall, 
the  ball  A  is  released  from  the  rod,  and  begins  to  fall.  The  sounds 
made  on  striking  the  floor  reach  the  ears  of  the  observer  at  the  same 
instant ;  this  shows  that  both  balls  reach  the  floor  in  sensibly  the  same 


68  MOLAR    DYNAMICS. 

time,  and  that  the  horizontal  motion  which  one  of  the  balls  has  does 
not  affect  the  time  of  its  fall,  i.e.  does  not  modify  the  effect  of  the  force 
of  gravity. 

The  law  implies,  (3)  that  if  two  or  more  forces  act  on  a 
body,  each  produces  its  own  change  of  momentum  in  its  own 
direction  independently  of  the  others.  It  declares,  what  we  have 
previously  learned,  that  the  operation  of  compounding  forces 


\ 

\  \ 


is  just  the  same  as  that  of  compounding  motions  which  the 
several  forces  tend  to  produce  in  the  same  time,  hence  the 
apparatus,  Fig.  6,  illustrates  either  the  composition  of  motions 
or  the  composition  of  the  forces  by  which  the  motions  are 
produced. 

Third  Law:  To  evert/  action  there  /x  an  efjitfil  find  opposite 
reaction. 

Previous  to  the  announcement  of  the  Laws  of  Motion  our 
studies  have  been  such  as  to  prepare  us  both  to  understand 
and  accept  them.  We  have  learned  that  there  are  always 
two  bodies  or  two  parts  of  the  same  body  oppositely  affected 
by  every  force.  When  the  double  aspect  of  a  force,  i.e.  its 


LAWS    OF    MOTION.  69 

mutual  action  between  two  portions  of  matter,  is  considered, 
it  is  customary  to  speak  of  the  force  as  a  stress.  Illustrations 
of  stress  are  tension  in  a  stretched  rubber  band  and  pressure 
exerted  between  two  bodies  in  contact  when  compressed.  All 
force  is  of  the  nature  of  a  stress  and  the  Third  Law  of  Motion 
virtually  declares  that  every  action  between  two  bodies  is  a 
stress.  When  the  effect  of  the  action  upon  only  one  of  the 
two  bodies  is  under  consideration,  the  action  is  commonly 
spoken  of  as  a  force. 

It  remains  to  show  that  action  and  reaction  are  equal.  That 
they  are  equal  is  deducible  from  the  First  Law,  for  if  they 
were  unequal,  then,  when  there  is  an  action  between  two 
parts  of  the  same  body,  there  would  not  be  equilibrium.  That 
is,  there  would  be  an  unbalanced  force,  which  would  cause 
the  body  to  move  with  accelerated  velocity  —  a  thing  which 
is  explicitly  contradicted  by  the  First  Law. 

If  action  and  reaction  were  not  equal  there  might  be  a 
possibility  that  a  person  might  raise  himself  by  pulling  on 
the  soles  of  his  feet  or  the  hair  of  his  head;  that  a  vessel 
might  be  propelled  in  a  calm  by  blowing  against  its  sail  with 
a  powerful  bellows  (operated  by  steam)  located  on  the  deck 
of  the  same  vessel ;  that  a  person  sitting  in  a  buggy  might 
give  himself  a  ride  by  pressing  his  feet  against  the  dasher ; 
that  a  person  might  advance,  i.e.  move  his  center  of  mass, 
without  the  earth  beneath  him ;  that  a  bird  might  fly  without 
the  external  air  to  act  on. 

In  case  the  two  bodies  are  free  from  the  action  of  resisting 
forces  the  law  implies  that  the  momenta  generated  by  the 
action  and  reaction  are  equal. 

The  application  of  this  law  is  not  always  obvious.  Thus, 
an  apple  falls  to  the  ground  in  consequence  of  an  action 
between  the  apple  and  the  earth.  The  motion  of  the  earth 
toward  the  apple  is  imperceptible.  But  this  is  because 
the  mass  of  the  earth  is  enormously  greater  than  that  of 


70  MOLAR   DYNAMICS. 

the   apple,   and   its   velocity,   for    an   equal   momentum,   is 
proportionately  less. 

Exercises. 

1.  a.  Why  does  not  a  given  force,  acting  the  same  length  of  time,  give 
a  loaded  car  as  great  a  velocity  as  an  empty  car  ?     b.  After  equal  forces 
have  acted  for  the  same  length  of  time  upon  both  cars,  and  have  given 
them  unequal  velocities,  which  will  be  the  more  difficult  to  stop  ? 

2.  a.  The  planets  move  unceasingly  ;  is  this  evidence  that  there  are 
forces  pushing  or  pulling  them  along  ?     b.  None  of  their  motions  are  in 
straight  lines ;  are  they  acted  upon  by  external  forces  ? 

3.  A  certain  body  is  in  motion  ;  suppose  that  all  hindrances  to  motion 
and  all  external  forces  be  withdrawn  from  it,  how  long  will  it  move  ? 
Why?     In  what  direction?     Why?     With  what  kind  of  motion,  i.e. 
accelerated,  retarded,  or  uniform  ?     Why  ? 

4.  Explain  how  rotating  lawn-sprinklers  are  kept  in  motion. 

5.  When  you  leap  from  the  earth,  which  receives  the  greater  momen- 
tum, your  body  or  the  earth  ? 

6.  When  you  kick  a  door-rock,  why  does  snow  or  mud  on  your  shoes 
fly  off  ? 

7.  If  a  man  in  a  boat  move  it  by  pulling  on  a  rope  at  one  end,  the 
other  end  being  fastened  to  a  post,  how  is  the  boat  put  in  motion  ? 
Would  it  move  either  faster  or  slower  if  the  other  end  were  fastened  to 
another  boat  free  to  move,  the  man  exerting  the  same  force  ? 

8.  An  ounce  bullet  leaves  a  gun  of  mass  8  pounds  with  a  speed  of  800 
feet  per  second.     What  is  the  maximum  speed  of  the  gun's  recoil  ? 

9.  Suspend  two  balls  of  soft  putty  of  equal  mass,  A  and  B  (Fig.  48). 
Draw  A  to  one  side,  and  let  it  fall  so  as  to  strike  B.     Both  balls  will  then 
move  on  together ;  with  what  momentum  compared  with  A's  momentum 
when  it  strikes  B  ? 

10.  What  will  be  the  momentum  of  each  ball  after  A  strikes  B,  com- 
pared with  A's  momentum  when  it  strikes  B  ? 

11.  How  will  their  velocity  compare  with  A's  velocity  when  it  strikes  B? 

12.  Kaise  A  and  B  equal  distances  in  opposite  directions,  and  let  them 
fall  so  as  to  collide.     Both  balls  will  instantly  come  to  rest  after  collision. 
Show  that  this  result  is  consistent  with  the  third  law  of  motion. 

13.  Substitute  for  the  inelastic  putty  balls,  ivory  billiard  balls,  which 
are  highly  elastic.     Let  A  strike  B.     Then  B  goes  on  with  A's  original 
velocity,  while  A  is  brought  to  rest.     Show  that  this  result  is  consistent 
with  the  third  law  of  motion. 


LAWS    OF    MOTION. 


71 


14.  Suspend  four  ivory  balls,  C,  D,  E,  and  F.     Let  C  strike  D.     B 
receives  all  of  C's  momentum,  instantly  communicates  it  to  E,  and  E  to 
F.    F,  having  nothing  to  which  to  communicate  the  momentum,  moves 
with  C's  original  velocity.     Trace  the  actions  and  reactions  throughout. 

15.  What  would  happen  if  the  four  balls  were  inelastic  ? 

16.  A  shell  at  rest  bursts  into  two  parts,  the  smaller  being  one-third  of 
the  whole  ;  what  is  the  ratio  of  the  initial  velocities  of  the  parts  ? 

17.  a.  Can  any  body,  animate  or  inanimate,  by  any  action  confined  to 


o 

A' 


oo  y  V'  y:    oooo    y 

ABABC  CDEF 


FIG.  48. 


itself,  i.e.  between  component  parts  of  itself,  put  itself  in  motion  or  stop 
itself  ?     6.  How  can  a  body  put  itself  in  motion  ? 

18.  A  child  sits  upon  a  sled.     The  sled  is  suddenly  started  and  the 
child  is  left  sitting  on  the  ice.     a.  Is  this  due  to  the  inertia  of  the  child  ? 
b.  Is  it  due  to  a  resistance  which  the  child's  body  offers  to  a  force  tending 
to  put  it  in  motion,  or  to  the  inadequacy  of  the  force  transmitted  to  it 
through  the  sled  to  give  its  mass  in  the  same  time  an  equal  velocity  with 
the  sled  ? 

19.  Why   do   not  heavy  bodies  fall  faster  in  a  vacuum  than  light 
ones  ? 

20.  Take  equal  masses  of  wood  and  lead  ;  which  weighs  more  ? 

21.  A  stone  falls  from  the  top  of  a  railway  carriage  which  is  moving  at 
the  rate  of  one-half  of  a  mile  a  minute.     Disregarding  the  resistance  of 
the  air,  find  what  horizontal  distance  and  what  vertical  distance  the  stone 
will  have  passed  through  in  one-tenth  of  a  second.   Ans.  4.4  ft.;  .16  ft. 


72 


MOLAR    DYNAMICS. 


SECTION  VIII. 

APPLICATIONS    OF    THE    LAWS    OF    MOTION. 
MOTION. 


CURVILINEAR 


64.  How  curvilinear  motion  is  produced.  —  Motion  is  curvi- 
linear when  its  direction  changes  at  every  point.  But  according 
to  the  first  law  of  motion,  every  moving  body  proceeds  in  a 
straight  line  unless  compelled  to  depart  from  it  by  some 
external  force.  Hence  curvilinear  motion  can  be  produced 
only  by  an  external  force  acting  continuously  upon  the  body 
at  an  angle  to  the  straight  path  in  which  the  body  tends  to 
move,  so  as  constantly  to  change  its  direction.  In  case  the 
body  moves  in  a  circle,  this  force  acts  at  right  angles  to  the 
path  of  the  body  or  towards  the  center  of  motion ;  hence  this 
deflecting  force  has  received  the  name  of  central  force. 

Thus,  suppose  a  ball  at  A  (Fig.  49),  suspended  by  a  string 
from  a  point  d,  to  be  struck  by  a  bat, 
in  a  manner  that  would  cause  it  to 
move  in  the  direction  Ao.  At  the 
same  time  it  is  restrained  from  taking 
that  path  by  the  tension  of  the  string, 
>fl  which  operates  like  a  force  drawing 
it  toward  d.  It  therefore  takes,  in 
obedience  to  the  two  forces,  an  inter- 
mediate course.  At  c  its  motion  is 
in  the  direction  en,  in  which  path  it 
would  move  but  for  the  string,  in  accordance  with  the  first 
law  of  motion.  Here,  again,  it  is  compelled  to  take  an  inter- 
mediate path.  Thus,  at  every  point,  the  tendency  of  the 
moving  body  is  to  preserve  the  direction  it  has  at  that  point, 
and  consequently  to  move  in  a  straight  line.  The  only  reason 
it  does  not  so  move  is  that  it  is  at  every  point  forced  from  its 
natural  path  by  the  pull  of  the  string.  But  if,  when  the  ball 


MAGNITUDE    OF    CENTRAL    FORCE.  73 

reaches  the  point  i,  the  string  be  cut,  the  ball,  having  no 
force  operating  to  change  its  motion,  continues  in  the  direction 
in  which  it  is  moving  at  that  point,  i.e.  in  the  direction  ih, 
which  is  tangent  to  its  former  circular  path. 

65.  Magnitude  of  central  force  for  bodies  moving  in  circular 
paths. 

Experiment  1.  —  Cause  a  ball  to  revolve  around  your  hand  by  means  of 
a  string  attached  to  it  and  held  in  the  hand.  Observe  closely  every  phase 
of  the  operation.  First  you  make  a  movement  as  if  to  project  the  ball 
in  a  straight  line.  Immediately  you  begin  to  pull  on  the  string  to  prevent 
its  going  in  a  straight  line.  Under  the  continuous  influence  of  these  two 
forces  in  a  short  time  the  ball  acquires  great  speed.  You  may  now  cease 
to  exert  any  projecting  force,  and  simply  keep  the  hand  still ;  but  as  the 
ball  has  acquired  a  motion,  and  all  motion  tends  to  be  in  a  straight  line, 
you  are  still  obliged  to  exert  a  pulling  force  to  deflect  it  from  its  path. 
Observe  that,  as  the  velocity  of  the  ball  is  retarded  by  the  resistance  of 
the  air,  the  pulling  or  deflecting  force  which  you  are  obliged  to  employ 
rapidly  diminishes. 

To  satisfy  yourself  that  the  ball  tends  to  move  in  a  straight  line,  let  go 
the  string  or  cut  it,  and  the  ball  immediately  moves  off  in  a  straight  line, 
or  simply  perseveres  in  the  direction  it  had  at  the  instant  the  string  was 
cut,  Observe  that  the  ball  appears  while  rotating  to  be  pulling  your  hand  • 
but  you  know  that  all  the  force  concerned  originates  in  yourself,  and  that 
this  apparent  pull  on  the  part  of  the  ball  is  only  the  effect  of  the  reaction 
of  the  force  which  you  exert  on  the  ball.  This  reactionary  or  centrifugal 
tendency  is  erroneously  called  "  centrifugal  force."  J 

Every  revolving  body  affords  an  example  of  central  force 
and  centrifugal  tendency.  Hence  we  say  that  every  revolving 
body  tends  to  fly  away  from  the  center  (not  radially,  however, 
but  tangentially),  and  a  central  force  is  required  to  keep  the 
body  in  its  circular  path. 

When  you  swing  the  ball  about  your  hand  you  discover 
that  the  force  of  the  pull  increases  with  the  velocity,  and 
more  rapidly  than  the  velocity.  Careful  observations  have 

1  There  is  no  centrifugal  force.  The  only  force  exerted  is  the  central  force,  which 
is  of  such  a  magnitude  as  to  change  the  direction  of  the  momentum  just  fast  enough 
to  keep  the  hody  moving  in  a  circle. 


74 


MOLAR   DYNAMICS. 


determined  that  for  bodies  revolving  in  circular  orbits  the 
central  force  varies  as  the  mass  of  the  body,  as  the  square  of  its 
velocity,  and  inversely  as  its  distance  from  the  center. 

Let  a  point  move  uniformly  in  the  circular  path  0  P  Q  (Fig.  49a), 
traversing  the  distance  O  P  in  time  t  ; 
then  0  P  =  0  t  (1).  If  P  be  very  near 
O,  the  deflection  T  P  from  a  straight 
line  due  to  the  central  force  is  ap- 
proximately equal  to  ON.  If  a  be 
the  acceleration  towards  the  center 
due  to  this  force,  ON  =  £a£2  (2). 
But  by  geometry  OP2  =  ON-OD. 
Comparing  (1)  and  (2),  we  get  v2tz 

v2 

=  I  a  t2  •  2  r,  or  a  =  —  .     Since  F  = 
r 

V2 

m  a,  we  get  F  =  ra  —  . 


FIG.  49a. 


The  farther  a  point  is  from  the  axis  of  motion  of  a  rigid 
body,  the  farther  it  has  to  move  during  a  rotation  ;  con- 
sequently the  greater  its  velocity.  Hence,  bodies  situated  at 
the  earth's  equator  have  the  greatest  velocity,  due  to  the 
earth's  rotation,  and  consequently  the  greatest  tendency  to  fly 
off  from  its  surface.  The  effect  of  this  is  to  neutralize,  in 
some  measure,  the  force  of  gravity.  It  is  calculated  that  a 
body  weighs  about  ^¥  less  at  the  equator  than  at  either  pole, 
in  consequence  of  the  greater  centrifugal  tendency  at  the 
former  place.  But  289  is  the  square  of  17;  hence,  if  the 
earth's  velocity  were  increased  seventeenfold,  objects  at  the 
equator  would  weigh  nothing,  i.e.  the  centrifugal  tendency 
would  be  equal  to  their  weight. 

The  attraction  between  the  sun  and  the  earth  causes  these 
bodies  to  move  in  curvilinear  paths,  performing  what  are 
called  annual  revolutions.  Were  it  not  for  this  mutual 
attraction  (and  the  attraction  of  the  other  celestial  bodies), 
the  motion  of  both  these  bodies  would  be  eternally  in  straight 


MAGNITUDE  OF  CENTRAL  FORCE.         75 

lines,  but  in  consequence  of  their  mutual  attraction  both 
rotate  about  a  point  C  (Fig.  50),  which  is  the  center  of  mass 
of  the  two  bodies  considered  as  one  body  (as  if  connected 
by  a  rigid  rod).1  If 
both  bodies  had  equal 
masses,  the  center  of 
gravity  and  center  of 
motion  would  be  half- 
way between  the  two 

bodies ;  but  as  the  mass  of  the  earth  is  less  than  that  of  the 
sun,  so  its  velocity  and  distance  traversed  are  proportionally 
greater.  In  reality  the  center  of  motion  C  is  within  the  sun 
near  the  edge  toward  the  earth. 

Experiment  2.  —  Apply  the  frame  T  (Fig.  51)  to  any  rotating  appa- 
ratus as  R  (Fig.  52)  so  that  it  may  be  rotated  about  its  axis  d.  The  rod  c 
passes  through  the  balls  a  and  b  loosely  so  that  the  latter  are  free  to 
slide  along  the  rod.  The  two  balls  are  connected  by  a  string  so  that 
they  are  compelled  to  rotate  as  one  body  or  one  system  of  bodies. 


I 


A 

—*jii 


FIG.  51. 

The  mass  of  a  is  twice  that  of  6.  Rotate  the  system,  and  show  that  there 
is  equilibrium  in  the  system  only  when  the  center  of  b  is  twice  as  far  from 
the  axis  of  rotation  as  the  center  of  a.  How  does  this  verify  the  above 
law  ?  While  there  is  rotation,  is  there  tension  in  the  string  connecting 
the  balls  ?  What  is  the  cause  of  an  action  between  the  balls  ?  Ball  a 
pulls  ball  b  ;  what  is  the  effect  of  this  pull  on  6  ?  What  is  the  effect  of 
the  reaction  on  a  ?  Is  there  a  similar  action  between  the  sun  and  earth  in 

1  Strictly  speaking,  the  earth  does  not  revolve  around  the  sun  any  more  than  the 
sun  around  the  earth ;  but  both  rotate  about  their  common  centroid. 


76 


MOLAR    DYNAMICS. 


their  annual,  re  volutions  ?  By  what  name  is  the  action  known  ?  If  the 
sun  or  the  earth  were  instantaneously  annihilated,  state  what  would 
happen  to  the  other  body  if  it  were  left  entirely  free,  i.e.  if  its  motion 
were  not  affected  by  other  bodies  in  the  universe  ? 


FIG 

Experiment  3.  —  Arrange  some  kind  of  rotating  apparatus,   e.g.   "R 
(Fig.  52).     Suspend  a  skein  of  thread  a  (Fig.  53)  by  a  string,  and  cause 

it  to  rotate  ;  it  assumes  the  shape  of 
the  oblate  spheroid  a'.  Mount  a  glass 
globe  G  (Fig.  52)  about  one-tenth 
full  of  colored  water,  and  rotate. 
The  liquid  gradually  leaves  the  bot- 

tom' rises' and  f°rms  an  e(Juatoriai 

ring  within  the  glass.  This  illustrates 
the  probable  method  by  which  the 
earth,  on  the  supposition  that  it  was 
once  in  a  fluid  state,  assumed  its 
present  spheroidal  state.  (Explain.) 
Pass  a  string  through  the  longest  diameter  of  an  onion  c,  and  cause 
it  to  rotate  ;  the  onion  gradually  changes  its  position  so  as  to  rotate  on 
its  shortest  axis. 

It  can  be  demonstrated  mathematically,  as  well  as  experi- 
mentally, that  a  freely  rotating  lady  is  in  stable  equilibrium 


FIG.  53. 


THE   PENDULUM.  77 

only   when    rotating   about   its   shortest   diameter;    hence   the 
tendency  of  a  rotating  body  to  take  this  position. 

Questions. 

1.  a.  What  is  the  cause  of  the  stretching  force  exerted  on  the  rubber 
cord  when  you  swing  a  return  ball  about  your  hand  '?     6.  Suppose  that 
you  double  the  velocity  of  the  ball ;  how  many  times  shall  you  increase 
this  stretching  force  ? 

2.  In  what  way  can  the  tension  in  the  string  (Fig.  51)  be  so  much 
increased  as  to  break  it  ? 

3.  Why  do  wheels  and  grindstones,  when  rapidly  rotating,  tend  to 
break,  and  the  pieces  to  fly  off  ? 

4.  On  what  does  the  magnitude  of  the  pull  between  a  rotating  body 
and  its  center  of  motion  depend  ? 

5.  a.  Explain  the  danger  of  a  carriage  being  overturned  in  turning  a 
corner.      6.    How  many  fold  is  the  tendency  to  overturn  increased  by 
doubling  the  velocity  of  the  carriage  ? 

(>.    Account  for  the  curvilinear  orbits  of  the  planets. 

7.  How  are  their  motions  in  their  orbits  and  around  their  axes  main- 
tained f 

8.  In  what  way  should  the  rails  be  laid  so  as  to  neutralize  the  centrif- 
ugal tendency  of  a  railroad  train  going  around  a  curve  ? 

9.  State  and  explain  the  posture  of  a  bicycle  rider  in  turning  a  curve. 
-  10.    In  what  way  is  the  weight  of  terrestrial  bodies  nullified  in  some 

degree  by  the  earth's  motion  ? 

11.    A  circus  rider  going  around  a  ring  inclines  inward  so  that  the  line 
of  direction  of  his  body  falls  without  his  base.     How  is  he  supported  ? 

SECTION  IX. 

THE    PENDULUM. 

Experiment  1.  —  From  a  bracket  suspend  by  strings  leaden  balls,  as  in 
Fig.  54.  Draw  B  and  C  to  one  side,  and  to  different  hights,  so  that  B 
may  swing  through  a  short  arc,  and  let  both  drop  at  the  same  instant. 
C  moves  much  faster  than  B,  and  completes  a  longer  journey  at  each 
swing,  but  both  complete  their  swing,  or  vibration,  in  the  same  time. 

Hence,  (1)  the  time  occupied  by  the  vibration  of  a  pendulum 
is  independent  of  the  length  of  the  arc.  Of  only  very  small  arcs 


78 


MOLAR    DYNAMICS. 


may  this  law  be  regarded  as  practically  true.  The  pendulum 
requires  a  somewhat  longer  time  for  a  long  arc  of  vibration 
than  for  a  short  one,  but  the  difference  becomes  perceptible 
only  when  the  difference  between  the  arcs  is  great,  and  then 
only  after  many  vibrations. 

Experiment  2.  —  Set  all  the  balls  swinging ;  only  B  and  C  swing 
together;  the  shorter  the  pendulum,  the 
faster  it  swings.  Make  B  lm  long,  and 
F  Jm  long.  Watch  in  hand,  count  the 
vibrations  made  by  B.  It  completes  just 
60  vibrations  in  a  minute  ;  in  other  words, 
it  "  beats  seconds."  A  pendulum,  there- 
fore, to  beat  seconds  must  be  lm  long 
(more  accurately  in  the  latitude  of  Boston 
at  sea-level,  .9935™,  or  39.117  in.).  Count 
the  vibrations  of  F ;  it  makes  120  vibra- 
tions in  the  same  time  that  B  makes  60 
vibrations.  Make  G  one-ninth  the  length 
of  B ;  the  former  makes  three  vibrations 
while  the  latter  makes  one,  consequently 
the  time  of  vibration  of  the  former  is  one- 
third  that  of  the  latter. 

Hence,  (2)  the,  time  of  one  vibra- 
tion of  a  pendulum  varies  as  the 
square  root  of  its  length. 
The  length  I  of  a  simple  pendulum  to  swing  in  a  time  t,  or 
the  time  of  swing  for  a  length  I,  can  be  found  from  the 
formulae : 

T 


1 

77 

/ 

0 

G 

a< 

o 

J     &< 

c< 

o 

e 

) 

i 

• 

/c 

j 

1     C 

\    \ 

i    ( 
3    ( 

j 

FIG.  54. 

£=.9935  X  t'\  whence  t  = 


or      I  =  39.117  X  t2,  whence  t  = 


.9935 

~T 
39.117 


for  I  meters ; 


for  I  inches. 


The  isochronism  of  the  pendulum  is  utilized  in  the  measure- 
ment of  time,  i.e.  in  subdividing  the  solar  day  into  hours, 
minutes,  and  seconds.  The  office  of  the  pendulum  in 


ACCELERATING  FORCE  OF  GRAVITATION.      79 

clocks  is  to  regulate  the  rate  of  motion  of  the  works.  The 
balance-wheel  replaces  the  pendulum  in  watches  and  some 
clocks. 

66.  Determination  of  the  accelerating  force  of  gravitation  at 
any  locality.  —  The  time  of  vibration  is  less  at  a  place  where 
the  force  of  gravitation  is  greater  because  the  accelerating 
force  for  the  same  mass  is  greater  and  hence  the  pendulum 
will  move  faster. 

Hence  it  is  apparent  that  by  determining  the  time  of 
vibration  of  a  pendulum  1  of  the  same  length  at  different 
distances  from  the  center  of  mass  of  the  earth  (e.g.  at  the 
top  and  bottom  of  a  mountain,  or  at  sea-level  at  different 
latitudes),  the  relative  value  of  g  at  these  places,  i.e.  the 
acceleration  produced  by  gravitation,  may  be  ascertained. 
We  have  already  learned  that  the  acceleration  at  the  same 
locality  is  the  same  for  all  bodies  regardless  of  their  mass. 

By  experiments  too  difficult  for  ordinary  school  work,  it  has 
been  ascertained  that  (3)  the  time  of  vibration  of  a  pendulum 
varies  inversely  as  the  square  root  of  the  force  of  gravitation 
(upon  which  the  value  of  g  depends). 

To  sum  up  the  above  three  laws  of  the  pendulum,  we  have 
the  formula2 

n  ^i 

t  =  TT^-)  whence  g  =  — g-> 

i/ 

in  which  I  =  length  of  pendulum  ;  t  =  time  of  one  vibration 
in  seconds. 

1  The  following  measurement  of  g  was  made  with  great  care  occupying  months 
by  Mendenhall,  at  Tokio,  Japan,  in  the  year  1880.    The  latitude  of  this  place  is 
N.  35°  41';  value  of  g  at  sea-level  9.7984m ;   length  of  seconds-pendulum  994.59mm. 
On  the  summit  of  a  neighboring  mountain  12,441  feet  above  the  level  of  the  sea,  he 
found  the  time  of  vibration  of  the  same  pendulum  to  be  1.000336  seconds.    From  this 
he  computed  the  value  of  g  =  9.7886m.     He  also  calculated  the  attraction  of  the 
mountain  to  be  .00021  the  attraction  of  the  earth,  and  that  if  the  mountain  were 
annihilated,  at  that  altitude  g  would  be  equal  to  9.7865m. 

2  The  student  may  find  the  development  of  this  formula  in  Chapter  VII  of 
Maxwell's  "  Matter  and  Motion." 


80  MOLAR    DYNAMICS. 

At  the  poles  of  the  earth  the  length  of  a  seconds-pendulum 
is  99.62cm,  and  y  =  983.2cm  per  second.  At  the  equator, 
I  =  99.10cm ;  g  =  978.1cm  per  second  (Kohlrausch). 

07.    Center  of  oscillation. 

Experiment  3.  —  Connect  six  balls,  at  intervals  of  15cm,  by  passing  a 
wire  through  them,  after  the  manner  of  pendulum  A  (Fig.  54).  This 
forms  a  compound  pendulum  composed  of  six  simple  pendulums.  Set 
A  and  B  vibrating ;  A  vibrates  faster  than  B,  although  their  lengths  are 
the  same.  Why  is  this  ?  If  A  were  actuated  only  by  the  ball  /,  it  would 
vibrate  in  unison  with  B.  If  the  ball  a  were  free,  it  would  move  much 
faster  than  / ;  but,  as  they  are  constrained  to  move  together,  the  tendency 
of  a  is  to  quicken  the  motion  of  /,  and  the  tendency  of  /  is  to  check  the 
motion  of  a.  But  e  is  quickened  less  than  /,  and  d  less  than  e ;  on  the 
other  hand,  b  is  checked  by  /  less  than  a,  and  c  less  than  b.  It  is  apparent 
that  there  must  be  some  point  between  a  and  /  whose  motion  is  neither 
quickened  nor  checked  by  the  combined  action  of  the  balls  above  and 
below  it,  and  where,  if  a  single  ball  were  placed,  it  would  make  the  same 
number  of  vibrations  in  a  given  time  that  the  compound  pendulum  does. 
Shorten  pendulum  B,  and  find  the  required  point.  This  point  is  called 
the  center  of  oscillation. 

Every  compound  pendulum  is  equivalent  to  a  simple  pendulum 
whose  length  is  equal  to  the  distance  between  the  center  of 
oscillation  and  the  point  of  suspension  of  the  confound  pendulum 
Inasmuch  as  the  distance  between  the  point  of  suspension  and 
the  center  of  oscillation  determines  the  rate  of  vibration, 
whenever  the  expression  length  of  pendulum  is  used  it  must 
be  understood  to  mean  this  distance.  Strictly  speaking,  a 
simple  pendulum  is  a  heavy  material  point  suspended  by  a 
iveightless  thread.  Of  course  such  a  pendulum  cannot  actually 
exist ;  but  the  leaden  ball,  suspended  by  a  thread,  is  a  near 
approximation  to  it. 

Experiment  4.  —  Suspend  at  one  end  of  the  frame  (Fig.  54)  a  lath  AB 
(Fig.  55)  lm  long,  and  shorten  the  pendulum  B  till  it  swings  in  the  same 
period  as  the  lath ;  the  ball  of  B  marks  the  center  of  oscillation  of  the 
lath,  which  is  found  to  be  two-thirds  the  length  of  the  lath  below  the 
point  of  suspension.  Attach  a  pound-weight  to  the  lower  end  of  AB ; 


CENTER    OF    PERCUSSION. 


81 


B 


its  vibrations  are  now  slower,  and  the  simple  pendulum  B  must  be 
lengthened  to  vibrate  in  the  same  time  as  the  lath  and  weight ;  hence  the 
center  of  oscillation  of  the  lath  is  lowered  by  the  addition  of  the  & 
weight.  Move  the  weight  up  the  lath  ;  the  vibrations  are  quick- 
ened. (What  is  the  office  of  a  pendulum  bob  ?) 

Experiment  5.  —  Remove  the  weight,  bore  a  hole  through  the 
lath  at  its  center  of  oscillation  C,  and,  passing  a  knitting-needle 
through  the  hole,  invert  the  lath  and  suspend  it  by  the  needle. 
The  pendulum  is  now  apparently  shortened,  and  we  naturally 
expect  that  its  vibrations  will  be  quicker  than  when  suspended 
from  A.  But  the  part  B  C  now  vibrates  in  opposition  to  the  part 
CA,  rising  as  it  sinks,  and  sinking  as  it  rises.  This  tends  to 
check  the  rapidity  of  the  vibrations  of  C  A,  and  it  is  found  that 
the  pendulum  vibrates  in  the  same  time  when  suspended  from  FlG- t55- 
C  as  when  suspended  from  A.  The  point  of  suspension  and  the  center 
of  oscillation  are  interchangeable. 

68.    Center  of  percussion. 

Experiment  6.  —  Suspend  the  lath  by  a  string  attached  to  one  of  its 

extremities,  and  with  a  club 
strike  it  horizontally  near  its 
upper  extremity.  This  end  of 
the  lath  moves  in  the  direction 
of  the  stroke  (A,  Fig.  56),  at 
the  same  time  causing  a  sudden 
jerk  on  the  string,  which  is  felt 
by  the  hand.  Strike  the  lath 
in  the  same  direction,  near  its 
lower  extremity ;  the  upper 
end  of  the  lath  now  moves  in 
a  direction  opposite  to  the 
stroke  (B),  at  the  same  time 
causing  a  similar  jerk  of  the 
string.  Next  strike  the  lath  successively  at  points  higher  and  higher 
above  its  lower  extremity  ;  it  is  found  that  the  jerk  on  the  string  becomes 
less  till  the  center  of  oscillation  is  reached,  when  no  pull  on  the  string  is 
felt,  and  neither  end  of  the  lath  tends  to  precede  the  other,  but  both 
move  on  together  (C).  The  full  force  of  the  blow  is  spent  in  moving  the 
stick,  and  none  is  expended  in  pulling  the  string.  This  point  is  called 
the  center  of  percussion. 


FIG.  56. 


82 


MOLAR    DYNAMICS. 


The  center  of  percussion  is  coincident  with  the  center  of 
oscillation.  It  is  the  point  where  a  blow,  given  or  received,  is 
most  effective,  and  produces  the  least  stress  upon  the  support 
or  axis  of  motion.  The  base-ball  player  soon  learns  at  what 
point  on  his  bat  he  can  deal  the  most  effective  blow  to  the 
ball,  and  at  the  same  time  feel  the  least  tingle  in  his  hands. 

69.    Demonstration  of  the  earth's  rotation  on  its  axis. 

If  a  ball  and  string  pendulum  be  set  in  vibration  in  a  certain  plane, 

then  by  virtue  of  the  First  Law  of 
Motion  it  will  continue  to  vibrate 
in  the  same  plane  even  if  the  string 
is  twirled  so  that  the  ball  rotates 
on  its  axis.  If  the  pendulum  be 
suspended  from  the  ceiling  of  a 
cabin  in  a  vessel  and  the  vessel  be 
turned  completely  around,  the 
plane  of  vibration  will  not  be 
changed.  A  hammock  suspended 
on  deck  of  a  ship  retains  the  nor- 
mal position  independently  of  the 
roll  and  rock  of  the  ship,  i.e.  the 
hammock  does  not  swing,  but  the 
ship  supporting  the  hammock 
swings.  Now  if  a  graduated  cir- 
cle be  placed  just  beneath  the  ball, 
as  the  vessel  turns  about  the  ball 
will  cross  the  circle  at  different 
points  and  will  appear  to  be  chang- 
ing its  plane  of  vibration  ;  but  it 
FlG-  57-  is  evident  that  this  appearance  is 

deceptive,  and  that  the  graduated  circle  must  turn  around  with  the  vessel, 
and  that  the  pendulum  is  merely  pointing  out  the  angular  motion  of  the 
vessel.  In  the  same  manner  if  a  pendulum  were  suspended  at  one  of  the 
poles  of  the  earth,  in  24  hours  every  meridian  of  the  earth  would  be 
brought  beneath  it,  and  although  it  would  not  meanwhile  change  its 
plane  of  vibration,  it  would  appear  to  move  from  east  to  west,  or  in 
opposite  direction  to  that  of  the  earth,  at  the  rate  of  15°  per  hour.  At 
the  equator  there  would  be  no  change.  Between  the  equator  and  the 
pole  the  change  per  hour  would  vary  from  0°  to  15°  according  to  the 


EARTH'S  ROTATION  ON  ITS  AXIS.  83 

latitude.     With  a  heavy  metal  ball  and  a  wire  as  small  as  will  support 
the  ball  and  very  long  (Fig.  57),  one  may  successfully  repeat  this  cele- 
brated experiment,  by  which  Foucault  demonstrated  the  motion  of  the 
earth  on  its  axis. 
t 

Questions  and  Problems. 

1.  What  is  the  length  of  a  pendulum  that  beats  half-seconds?     Quar- 
ter-seconds ?    That  makes  one  vibration  in  two  seconds  ?     That  makes 
two  vibrations  per  minute  ? 

2.  State  the  proportion  that  will  give  the  number  of  vibrations  per 
minute  made  by  a  pendulum  40  cm  long. 

3.  Where  is  the  center  of  percussion  in  a  hammer  or  axe  ? 

4.  At  what  point  (disregarding  the  length  and  weight  of  the  striker's 
arm)  should  a  blow  be  dealt  with  a  bat  of  uniform  dimensions  when  held 
in  the  hand  at  One  extremity  ? 

5.  What  change  in  the  location  of  the  center  of  percussion  is  produced 
by  making  one  end  of  a  bat  heavier  than  the  other  ? 

6.  Which  end  of  a  bat,  the  heavier  or  the  lighter,  should  be  held  in 
the  hands  ?     Why  ? 

7.  One  pendulum  is  20  inches  long,  and  vibrates  four  times  as  fast  as 
another.     How  long  is  the  other  ? 

8.  a.  What  effect  on  the  rate  of  vibration  of  a  pendulum  has  the  weight 
of  its  bob  ?    6.  What  effect  has  the  length  of  the  arc  ?    c.  What  affects 
the  rate  of  vibration  of  a  pendulum  ? 

9.  How  can  you  quicken  the  vibration  of  a  pendulum  threefold  ? 

10.  A  clock  loses  time.     a.  What  change  in  the  pendulum  ought  to 
be  made  ?     b.  How  would  you  make  the  correction  ? 

11.  Two  pendulums  are  four  and  nine  feet  long  respectively.     While 
the    short    one    makes    one    vibration,    how  many   will  the   long  one 
make? 

12.  What  is  the  time  of  vibration  of  a  pendulum  (39.09  -r-  4  =)  9.77  in. 
long? 

13.  The  number  of  vibrations  made  by  a  given  pendulum  in  a  given 
time  varies  as  the  square  root  of  the  force  of  gravity.     Force  of  gravity 
at  any  place  is  expressed  by  the  value  of  g  (i.  e.  by  the  acceleration  which 
it  produces),     a.  If  at  a  certain  place  a  pendulum  39.09  in.  long  make 
3600  vibrations  in  an  hour,  and  the  value  of  g  be  32.16  ft.,  what  is  the 
acceleration  at  a  place  where  the  same  pendulum  makes  3590  vibrations 
in  the  same  time  ?     b.   Which  of  the  two  places  is  nearer  the  centroid  of 
the  earth  ? 


84  MOLAR    DYNAMICS. 

14.  Suggest  some  way  by  which  the  force   of  gravity  at  different 
latitudes  and  altitudes  may  be  determined. 

15.  A  pebble  is  suspended  by  a  thread  2  ft.  long  ;  required  the  number 
of  vibrations  it  will  make  in  a  minute. 


SECTION  X. 

WORK    AND    ENERGY. 

70.  Work.  —  Whenever  a  force  causes  a  change  of  motion 
or  maintains  motion  against  resistance  it  is  said  to  do  work. 
A  force  may  act  for  an  indefinite  time  without  doing  work ; 
for  example,  a  person  may  support  a  stone  for  a  time  and 
become  weary  from   the   continuous  application*  of  force  to 
prevent  its  falling,  but  he  does  no  work  because  he  effects  no 
change  of  motion  or  position.     A  force  to  do  work  must  effect 
a  change  of  position.     Force  and  space  are  essentials  of  work. 
Force  without  motion  is  not  work  ;  motion  without  force  is 
not  work.   The  planets  move,  but  do  not  work.    Let  the  person 
supporting  the  stone  exert  a  little  more  force,  —  the  stone 
will  rise  and  work  will  be  done.     An  unbalanced  force  always 
does  work. 

The  body  that  moves  another  body  is  said  to  do  work  upon  it ; 
and  the  body  moved  is  said  to  have  work  done  upon  it. 

When  the  heavy  weight  of  a  pile-driver  is  raised,  work  is 
done  upon  it ;  when  it  descends  and  drives  the  pile  into  the 
earth,  work  is  done  upon  the  pile,  and  the  pile  in  turn  does 
work  upon  the  matter  in  its  path. 

71.  Energy.  —  By  the    energy   of  a   body   is    meant    "  its 
capacity  for  doing  work"  (Maxwell).     It  is  measured  by  the 
quantity  of  work  which  the  body  possessing  it  is  capable  of 
doing ;  hence  the  unit  of  work  is  also  the  unit  of  energy.   The 
act  of  doing  work  consists  in  a  transfer  of  energy  from  the 
body  doing  work  to  the  body  on  which  work  is  done,  as  when 
the  wind  propels  a  vessel ;  or  it  consists  in  a  transformation 


KINETIC    AND    POTENTIAL    ENERGY.  85 

of  one  kind  of  energy  into  another  kind,  as  when  the  pile 
driver  strikes  the  pile  and  the  pile  is  forced  into  the  earth. 
Here,  a  part  of  the  energy  in  each  act  is  transformed  into 
heat,  which  we  shall  learn,  farther  on,  is  molecular  energy. 
Work,  therefore,  may  be  denned  as  the  act  of  transmitting  or 
transforming  energy. 

"  We  are  acquainted  with  matter  only  as  that  which  may  have 
energy  communicated  to  it  from  other  matter,  and  which  may  in  its 
turn  communicate  energy  to  other  matter.  Energy,  on  the  other 
hand,  we  know  only  as  that  which  in  all  natural  phenomena  is  con- 
tinually passing  from  one  portion  of  matter  to  another."  (MAXWELL.) 

72.  Kinetic  find  potential  energy.  Experience  teaches  that 
every  moving  body  can  impart  motion,  therefore  it  can  do 
work  upon  another;  hence  every  moving  body  possesses  energy. 
The  energy  which  a  body  possesses  in  consequence  of  its 
motion  is  called  kinetic  (motion)  energy.  It  is  a  property  of 
a  moving  mass  only.  It  is  capacity  for  doing  work  possessed 
by  a  mass  in  virtue  of  its  motion. 

When  a  body  is  projected  upward  its  kinetic  energy  dimin- 
ishes as  it  rises  and  finally  becomes  nil,  but  it  is  not  lost,  for 
it  is  regained  as  the  body  falls.  Its  energy  becomes,  while 
rising,  stored  up  in  virtue  of  its  higher  position.  Energy  in 
store,  i.e.  not  in  an  active  state,  is  called  potential  energy.  It 
is  the  capacity  for  doing  work  possessed  by  a  mass  in  virtue 
of  its  position  being  such  that  it  is  possible  for  it  to  move,  and  in 
virtue  of  the  existence  of  a  stress  which  tends  to  move  it.  Hence 
it  is  convertible  into  kinetic  energy  without  the  agency  of  any 
additional  work  except  to  remove  obstacles  to  the  conversion. 
Potential  or  positional  energy  implies  force,  or  a  tendency  to 
motion,  as  truly  as  kinetic  energy  implies  motion. 

Illustrations  of  energy  in  the  potential  state : 

(1)  A  stone  lying  on  the  ground  is  devoid  of  energy.  Raise 
it  and  place  it  on  a  shelf ;  in  so  doing  you  perform  work  upon 


86  MOLAK    DYNAMICS. 

it.  As  you  look  at  it  lying  motionless  upon  the  shelf,  it 
appears  as  devoid  of  energy  as  when  lying  on  the  earth. 
Attach  one  end  of  a  cord  to  it  and  pass  it  over  a  pulley  and 
wind  a  portion  of  the  cord  around  the  shaft  connected  with  a 
sewing-machine,  lathe,  or  other  convenient  machine.  Suddenly 
withdraw  the  shelf  from  beneath  the  stone.  The  stone  moves  ; 
it  communicates  motion  to  the  machinery,  and  you  may  sew, 
turn  wood,  etc.,  with  the  energy  given  to  the  machine  by  the 
stone. 

The  work  done  on  the  stone  or  the  energy  transmitted  to 
the  stone  in  raising  it,  was  not  lost ;  it  was  recovered  while 
the  stone  was  descending.  There  is  a  very  important  differ- 
ence between  the  stone  lying  on  the  ground,  and  the  stone 
lying  on  the  shelf :  the  former  is  powerless  to  do  work ;  the 
latter  can  do  work.  Both  are  alike  motionless,  and  you  can 
see  no  difference,  except  an  advantage  that  the  latter  has  over 
the  former  in  having  a  position  such  that  it  can  move.  What 
gave  it  this  advantage  ?  Work.  A  body,  then,  may  possess 
energy  due  merely  to  ADVANTAGE  OF  POSITION.,  derived  always 
from  work  performed  upon  it.  We  see,  then,  that  energy  may 
exist  in  either  of  two  widely  different  states.  It  may  exist 
in  bodies  by  virtue  of  their  actual  motion,  or  it  may  exist  in 
bodies  by  virtue  of  their  having  an  opportunity  to  move,  as  in 
the  stone  lying  on  the  shelf. 

Possibly  some  will  object  that  the  work  done  is  performed 
by  gravity,  and  not  by  the  stone's  energy ;  that  if  this  force 
should  cease  to  exist,  the  stone  would  not  move  if  the  shelf 
were  removed,  and  consequently  no  work  would  be  done.  All 
this  is  very  true,  and  it  is  likewise  true  that  when  the  stone 
is  on  the  ground  the  same  force  of  gravity  is  acting,  but  can 
do  no  work  simply  because  the  position  of  things  is  such  that 
the  stone  cannot  move.  The  energy  which  the  stone  on  the 
shelf  possesses  is  due  to  the  fact  that  its  position  is  such  that 
it  can  move,  and  that  there  is  a  stress  between  it  and  the  earth 


KINETIC    AND    POTENTIAL    ENERGY.  87 

which  will  cause  it  to  move.  Both  advantage  of  position  and 
stress  are  necessary,  but  the  former  is  attained  only  by  work 
performed.  The  force  of  gravity  is  employed  to  do  work,  as 
when  mills  are  driven  by  falling  water  ;  but  the  water  must 
first  be  raised  from  the  ocean-bed  to  the  hillside  by  the  work 
of  the  sun's  heat.  The  elastic  force  of  springs  is  employed 
as  a  motive  power  :  but  this  power  is  due  to  an  advantage  of 
position  which  the  molecules  of  the  springs  have  first  acquired 
by  work  done  upon  them. 

We  are  as  much  accustomed  to  store  up  energy  for  future 
use  as  to  store  up  provisions  for  the  winter's  consumption. 
We  store  it  when  we  wind  up  the  spring  or  weight  of  a  clock, 
to  be  doled  out  gradually  in  the  movements  of  the  machinery. 
We  store  it  when  we  bend  the  bow,  condense  air,  or  raise 
any  body  above  the  earth's  surface. 

(2)  Matter  may  possess  potential  energy  in  virtue  of 
chemical  separation  and  chemical  affinity,  and  the  potential 
energy  is  a  measure  of  the  work  done  in  effecting  the  sepa- 
ration. For  example  :  the  entire  value  of  coal  consists  in  its 
potential  energy,  which  was  stored  up  by  the  work  performed 
through  the  agency  of  the  sun's  energy  in  separating  the 
carbon  of  carbon  dioxide  from  the  oxygen.  Gunpowder  pos- 
sesses, in  a  dormant  state,  energy  sufficient  to  do  a  quantity 
of  work,  e.g.  in  blasting,  which  would  require  many  laborers 
a  long  time  to  do. 

A  body  2>ossesses  potential  energy  when,  in  virtue  of  work  done 
upon  it,  it  occupies  a  position  of  advantage,  or  its  constituent 
particles  occupy  positions  of  advantage,  so  that  the  energy  ex- 
pended can  be  at  any  time  recovered  by  the  return  of  the  body  to 
its  original  position,  or  by  the  return  of  its  particles  to  their 
original  positions. 

73.  Relation  of  energy  to  force  and  matter.  —  Our  discussions  lead 
us  to  conclude  that  energy  is  a  condition  of  matter,  due  either  to  its 
motion  or  to  its  relation  with  other  matter,  in  virtue  of  which  the  matter 


88  MOLAR    DYNAMICS. 

is  capable  of  doing  work.     Force l  may  be  regarded  as  ' '  the  measure 
of  the  tendency  of  energy"  to  transfer  or  "to  transform  itself." 

(TAIT.) 

Energy  is  never  found  except  in  association  with  matter.  Hence 
matter  may  be  defined  as  the  vehicle  or  receptacle  of  energy.  The 
First  Law  of  Motion  affirms  that  matter  is  simply  passive,  inert. 

74.  Practical  units  of  work  and  energy.  —  Inasmuch  as  a 
body's  capacity  to  do  work  is  dependent  wholly  upon  the  work 
which  has  been  done  upon  it,  it  is  evident  that  both  work  and 
energy  may  be  measured  by  the  same  unit.  The  practical 
unit  adopted  is  the  work  done  or  energy  imparted  in  raising  one 
pound  through  a  vertical  hight  of  one  foot.  It  is  called  a  foot- 
pound. The  metric  unit  is  the  work  done  or  energy  imparted 
in  raising  1  K  a  vertical  hight  of  1  m,  and  is  called  a  kilogram- 
meter.  The  kilogram  meter  is  equivalent  to  7.2331  ft.  Ibs. 
Since  the  work  done  in  raising  1  pound  1  foot  high  is  1  foot- 
pound, the  work  of  raising  1  pound  10  feet  high  is  10  foot- 
pounds, which  is  the  same  as  the  work  done  in  raising  10 
pounds  1  foot  high  ;  and  the  same,  again,  as  raising  2  pounds 
5  feet  high. 

There  are  many  kinds  of  work  besides  that  of  raising 
weights.  But  since,  with  the  same  resistance,  the  work  of 
producing  motion  in  any  other  direction  is  just  the  same  as 
in  a  vertical  direction,  it  is  easy,  in  all  cases  in  which  the 
resistance  and  space  through  which  the  resistance  is  overcome 
are  known,  to  find  the  equivalent  in  work  done  in  raising  a 
weight  vertically.  By  thus  securing  a  common  standard  for 
measurement  of  work,  we  are  able  to  compare  any  species  of 
work  with  any  other.  For  instance,  let  us  compare  the  work 
done  in  sawing  through  a  stick  of  wood  by  a  man  whose  saw 

1  •'  By  a  convenient  form  of  speech  a  given  force  is  said  to  act  upon  a  given  body 
and  to  impart  to  it  a  given  acceleration.  It  must  be  constantly  borne  in  mind,  how- 
ever, that  a  force  is  not  a  physical  entity,  and  can  never  be  measured  until  we 
already  know,  absolutely  or  by  comparison,  the  mass  acted  upon  and  the  acceleration 
imparted  to  it."  (DANIELL.)  "  Force  is  a  mere  phantom  suggestion  of  our  muscular 
sense."  (TAIT.)  "  Energy  has  its  price,  force  has  not." 


ABSOLUTE    UNITS    OF    WORK. 


89 


must  move  10  m  against  an  average  resistance  of  12  K,  with 
that  done  by  a  bullet  in  penetrating  a  plank  to  a  depth  of 
2  cm  against  an  average  resistance  of  200  K.  Moving  a  saw 
10  m  against  12  K  resistance  is  equivalent  to  raising  12  K 
mass  10  m  high,  or  doing  120  kgm  of  work ;  a  bullet  moving 
2  cm  against  200  K  resistance  does  as  much  work  as  is  re- 
quired to  raise  200  K  mass  2  cm  high,  or  200  X  .02=4  kgm 
of  work.  120-r-4  =  30  times  as  much  work  done  by  the 
sawyer  as  by  the  bullet. 

75.  Absolute  units  of  work.1  —  If  force  be  measured  in  dynes, 


Absolute 


Gravitation 
FIG.  58. 

and  distance  in  centimeters,  the  work  done  is  expressed  in  a 
C.G.S.  unit  called  an  erg.  An  erg  is  the  work  done  or  energy 
imparted  by  a  force  of  one  dyne  working  through  a  distance  of 
one  centimeter. 

In  purely  scientific  investigations  absolute  units  are  em- 
ployed. 

1  The  pupil  will,  perhaps,  be  assisted  by  the  accompanying  diagram  (Fig.  58)  in 
his  first  attempts  te  acquire  and  classify  the  units  of  force,  energy,  and  work  in  the 
several  systems. 


90  MOLAR   DYNAMICS. 

The  following  equivalents  will  be  useful  : 

Gravitation  units  absolute  units 

1  gram-centimeter  =0=  g  ergs, 

1  kilogrammeter     =c=  100,000  g  ergs, 

1  foot-pound  =  0.13825  X  105  X  g  ergs. 

76.  Formulas  for  calculating  work  or  energy  imparted.  — 
Force  and  space  (or  distance),  being  essentials  of  work  (p.  84), 
are  necessarily  the  quantities  employed  in  calculating  work. 
A  given  force  acting  through  a  space  of  one  foot  does  a  certain 
quantity  of  work;  it  is  evident  that  the  same  force  acting 
through  a  space  of  two  feet  would  do  twice  as  much  work. 
Hence  the  general  formula 

W=ft,  (1) 

in  which  f  represents  the  force  employed,  s  the  space  through 
which  the  force  acts,  and  W  the  work  done. 

In  case  a  force  encounters  resistance,  the  magnitude  of  the 
force  necessary  to  produce  motion  varies  with  the  resistance 
(Third  Law  of  Motion).  Often  the  work  done  upon  a  body  is 
more  conveniently  determined  by  multiplying  the  resistance  by 
the  space  through  ivhich  it  is  overcome,  and  our  formula  becomes 
by  substitution  of  r  (resistance)  for  /  (the  force  which  over- 
comes it) 

rs=W:  (2) 

For  example,  a  ball  is  shot  vertically  upward  from  a  rifle  in  a 
vacuum  ;  the  work  done  upon  the  ball  (by  the  explosive  force 
of  the  gunpowder)  may  be  calculated  by  multiplying  the 
average  force  (difficult  to  ascertain)  exerted  upon  it,  by  the 
space  through  which  the  force  acts  (a  little  greater  than  the 
length  of  the  barrel);  or  by  multiplying  the  resistance  to 
motion  offered  by  gravity,  i.e.  its  weight  (easily  ascertained), 
by  the  distance  the  ball  ascends. 


CALCULATING  WORK  OR  ENERGY  IMPARTED.    91 

Let  us  calculate  the  energy  stored  in  a  bow  by  an  archer 
whose  hand,  in  bending  the  bow  by  pulling  on  the  string, 
moves  6  inches  (-J-  foot)  against  an  average  resistance  of 
20  pounds.  Here  rs  =  20  X  i  — 10  foot-pounds  of  work  done 
upon  the  bow,  or  10  foot-pounds  of  energy  stored  in  the  bow. 

77.  .Formula  for  calculating  kinetic  energy.  —  Suppose  a  body 
to  have  a  mass  m  and  a  velocity  v ;  it  can  do  a  definite 
quantity  of  work  before  it  is  thereby  brought  to  rest.  If  it 
be  moving  upward  a  mutual  work  between  it  and  the  earth  is 
performed  in  destroying  each  other's  momenta.  If  its  velocity 
be  such  that  it  will  rise  to  a  hight  s,  then  its  kinetic  energy 
is  such  that  it  will  do  m  g  s  absolute  units  of  work,  or 

Eic  (Kinetic  energy)  =  m  g  s.  (1) 

We  may  find,  then,  to  what  vertical  hight  a  body  having 
a  given  velocity  would  rise  if  directed  upward,  and  from 
formula  (1)  determine  its  kinetic  energy ;  but  a  formula  may 
be  obtained  which  will  give  the  same  result  with  less  trouble  ; 
thus,  substituting  g  for  a  in  the  formula  v  =  at  (page  10),  we 
have  v  =  ytj  whence 

v  2 v2 

g '  g2 

Again  s=%gt2;  substituting  the  value  of  t2  in  this  equation 
we  have 

v2       v2 


9       *9 
Substituting  for  s  in  equation  (1)  its  value  we  have 

mv2 
^*  =  ~2-'  (2) 

a  formula  which  will  determine  the  kinetic  energy  of  a  body 
in  absolute  units  when  its  mass  and  velocity  are  known,  since 
the  energy  is  the  same  whatever  be  the  direction  of  the 
motion. 


92  MOLAK   DYNAMICS. 

Hence  the  kinetic  energy  of  a  body  is  half  the  product  of  its 
mass  by  the  square  of  its  velocity. 

if  the  result  be  desired  in  gravitation  units,  i.e.  in  gram- 
centimeters  or  foot-pounds,  the  number  of  absolute  units  must 
be  divided  by  g,  since  g  ergs  (980)  are  equivalent  to  one 
gram-centimeter,  or  g  foot-poundals  (32.2)  are  equivalent  to 
one  foot-pound. 

Work  done  by  a  force  is  measured  by  the  product  of  the  numeric 
of  the  force  and  that  of  the  space  s  or  [L]  through  which  it  acts. 
Then  since  force  [/]  =  [MLT~2],  the  dimensional  formula  for 
work  [W]  or  energy  [E]  is,  therefore,  (fs=)  [ML2T~2]. 

78.  Energy  contrasted  with  momentum.1  —  It  is  evident  from 
formula  (2)  that  when  the  mass  (m)  of  a  body  remains  the 
same,  its  energy  is  proportional  to  the  square  of  its  velocity ; 
while  its  momentum,  as  we  have  learned,  is  proportional  to  its 
velocity.  In  other  words,  the  effect  of  increasing  the  velocity 
of  a  moving  body  would  seem  to  be  to  increase  its  working 
power  much  more  rapidly  than  its  momentum.  Is  this  prac- 
tically true  ? 

Experiment.  —  Fill  a  water-pail  with  moist  clay.  Let  a  leaden  bullet 
drop  upon  the  clay  from  a  hight  of  .5m.  Then  drop  the  same  bullet 

1  Problem.  —  A  bullet  weighing  30  g  is  shot  with  a  velocity  of  98  in  per  second  from 
a  gun  weighing  4  K  ;  required  the  momentum  and  the  energy  of  both  the  bullet  and 
the  gun,  and  the  velocity  of  the  gun.  Solution:  Using  the  kilogram,  the  meter,  and 
the  second  as  units,  the  momentum  of  the  ball  is  .03  x  98  =  2.94  units.  If  the  ball 
were  shot  vertically  upward,  its  velocity  would  diminish  9.8  in  per  second  ;  so  it  would 

rise  —  =  10  seconds,  and,  therefore,  before  its  energy  was  expended,  to  a  hight  of 

(§  13)  4.9  in  x  102  =  490m.  Hence,  its  energy  at  the  outset  is  .03  x  490  =  14.7  kgm.  By 
the  third  law  of  motion  the  momentum  of  the  gun  must  be  just  the  same  as  that  of 
the  ball,  2.94  units;  its  velocity  is  therefore  2.94  -f-  4=  .735m  per  second.  Then 

735 
t  =  ~ —  =  .075  second  ;  the  hight  (supposing  the  gun  to  be  raised  vertically  by  the 

impulse  received)  =  4.9  x  .0752  =  .02766m  ;  and  its  energy  =  4  x  .02766  =  .1102  kgm. 
While,  therefore,  the  momenta  generated  in  the  two  bodies  by  the  burning  of  the 

powder  are  equal,  the  energy  of  the  bullet  is  — j—  =  133£  times  that  of  the  gun. 

(Why  are  the  effects  produced  by  the  bullet  more  disastrous  than  those  produced  by 
the  recoil  of  the  gun  ?) 


ENERGY    CONTRASTED    WITH    MOMENTUM.  93 

from  a  hight  of  2m,  or  four  times  the  former  hight,  in  order  that  it  may 
acquire  twice  the  velocity.  In  the  latter  case  it  penetrates  to  four  times 
the  depth  that  it  did  in  the  former. 

So  it  appears  that  the  energy  of  a  moving  body  varies,  not  as 
its  velocity,  but  as  the  square  of  its  velocity.  Doubling  the 
velocity  increases  the  energy  fourfold,  trebling  the  velocity 
increases  it  ninefold,  and  so  on  ;  but  the  corresponding 
momentum  is  increased  only  twofold,  threefold,  etc.  A  bullet 
moving  with  a  velocity  of  400  feet  per  second  will  penetrate, 
not  twice,  but  four  times,  as  far  into  a  plank  as  one  having  a 
velocity  of  200  feet  per  second.  A  railway  train  having  a 
velocity  of  20  miles  an  hour  will,  if  the  steam  be  shut  off, 
continue  to  run  four  times  as  far  as  it  would  if  its  velocity 
were  10  miles  an  hour.  The  reason  is  now  apparent  why 
light  substances,  even  so  light  as  air,  exhibit  great  energy 
when  their  velocity  is  great. 

Furthermore  we  have  seen,  p.  37,  that  momentum  —  M  V 
=ft-j  and  again,  p.  90,  W  (work  done)  or  Ek  (kinetic 
energy  imparted)  =fs. 

The  momentum,  then,  imparted  to  a  body  is  the  product  of 
the  force  into  the  time  it  acts;  energy  imparted  is  the  product 
of  force  into  the  space  through  which  it  acts.  It  is  evident, 
therefore,  that  force  may  be  measured  by  the  momentum  when 
time  is  considered,  and  by  the  energy  which  it  imparts  when  the 
space  is  considered. 

Questions  and  Problems.  • 

1.  Does  the  energy  expended  in  raising  the  stones  to  their  places  in 
the  Egyptian  pyramids  still  reside  in  the  stones  ? 

2.  What  kind  of  energy  is  that  contained  in  gunpowder? 

3.  Can  a  person   lift   himself,    or  put   himself   in   motion,    without 
exerting  force  upon  some  other  body  ? 

4.  a.  Can  a  body  do  work  upon  itself?     b.  Can   a  body  generate 
energy  in  itself,  i.  e.  increase  its  own  energy  ? 


94  MOLAR    DYNAMICS. 

5.  a.  Suppose  that  an  average  force  of  25  pounds  is  exerted  through 
a  space  of  10  inches  in  bending  a  bow ;  what  amount  of  energy  will  it 
give   the   bow  ?     b.    What  kind  of  energy  will   the   bow,   when  bent, 
possess  ? 

6.  a.  What  amount  of  kinetic  energy  does  a  mass  of  20  pounds  moving 
with  a  velocity  of  300  feet  per  second,  possess  ?    b.  What  amount  of  work 
can  the  body  do  ? 

7.  How  many  fold  is  the  kinetic  energy  of  a  body  increased  by 
doubling  its  velocity  ? 

""     8.    How  high  will  twelve  hundred  foot-pounds  of  energy  raise  100 
pounds  ? 

9.  A  force  of  500  pounds  acts  upon  a  body  through  a  space  of  20  feet. 
One-fourth  of  the  work  is  wasted  in  consequence  of  resistances.     How 
much  available  energy  is  imparted  to  the  body  ? 

10.  How  much  energy  is  stored  in  a  body  weighing  1,000  pounds,  at  a 
hight  of  200  feet  above  the  earth  ? 

11.  A  horse  draws  a  carriage  on  a  level  road  r ':  the  uniform  rate  of 
5  miles  an  hour.     a.  Does  work  accumulate  ?     b.  What  kind  of  energy 
does  the  carriage  possess  ?     c.  Suppose  that  the  carriage  were  drawn  up 
a  hill ;   would  energy  accumulate  ?     d.  What  kind  of  energy  would  it 
possess  when  at  rest  on  the  top  of  the  hill  ?     e.  How  would  you  calculate 
the  quantity  of  energy  it  possesses  when  at  rest  on  top  of  the  hill? 
/.  Suppose  that  the  carriage  is  in  motion  on  top  of  the  hill ;  what  two 
formulas  would  you  employ  in  calculating  the  total  energy  which   it 
possesses  ? 

12.  How  much  work  is  done  per  hour  if  80  K  be  raised  4m  per 
minute  ? 

13.  a.    What  energy  must  be  imparted  to  a  body  weighing  50  g 
that  it  may  ascend  4  seconds?     b.  How  many  times  as  much  energy 
must  be   imparted  to  the  same  body  that  it  may  ascend  5  seconds? 
c.  Why? 

14.  Compare  the  momenta,  in  the  two  cases  given  in  the  last  question, 
at  the  instants  the  body  is  thrown. 

15.  How  much  energy  is  stored  in  a  body  which  weighs  50  K,  at  a 
hight  of  80  m  above  the  earth's  surface  ? 

16.  How  much  kinetic  energy  would  the  same  body  have  if  it  had  a 
velocity  of  100  m  per  second  ? 

17.  Suppose  it  to  fall  in  a  vacuum,  how  much  kinetic  energy  would  it 
have  at  the  end  of  the  fourth  second  ? 

18.  If  it  should  fall  through  the  air,  what  would  become  of  a  part  of 
the  energy  ? 


ACTIVITY.  95 

19.  A  projectile  of  mass  25  K  is  thrown  vertically  upward  with  an 
initial  velocity  of  29.4  m  per  second.     How  much  energy  has  it  ? 

20.  What  becomes  of  its  energy  during  its  ascent  ? 

21.  a.  Compare  the  momentum  of  a  mass  50  K  having  a  velocity  of 
2m  per  second,  with  the  momentum  of  a  body  of  a  mass  50  g  having 
a  velocity  of  100  m  per  second,     b.  Compare  their  energies. 

22.  Which,  momentum  or  energy,  will  enable  one  to  determine  the 
amount  of  resistance  that  a  moving  body  may  overcome  ? 

23.  Explain  how  a  child  who  cannot  lift  30  K  can  draw  a  carriage 
weighing  150  K. 

24.  How  many  and  what  transformations  take  place  during  a  single 
swing  of  a  pendulum  ? 

25.  What  quantity  of  energy  will  be  expended  if  a  force  of  601bs. 
move  a  body  a  distance  of  20  ft.  ? 

26.  A  body  of  mass  30  Ibs.  moving  with  a  velocity  of  50  ft.  per  sec. 
must  do  how  much  work  before  it  stops  ? 

27.  A  United  States  12-inch  army  gun,  using  a  charge  of  440  Ibs.  of 
powder,  throws  a  projectile  of  mass  1000  Ibs.  with  an  initial  velocity  of 
1975  ft.  per  second,     a.  What  quantity  of  energy  is  imparted  to  the 
projectile  ?     b.  The  maximum  range  of  this  gun  is  15  miles.      If  the 
velocity  of  the  projectile  were  uniform,  in  how  many  seconds  would  it 
strike  the  ground  ?    c.  If  the  projectile  were  directed  vertically  upward, 
during  how  many  seconds  would  it  rise,  the  resistance  of  the  air  being 
disregarded  ?     d.  How  high  would  it  rise  ? 

28.  a.  A  street  car  having  a  mass  of  3  tons  was  moving  at  the  rate  of 
6  miles  per  hour.     The  brakes  were  applied  and  stopped  it  in  4  seconds. 
What  was  the  average  force  exerted  by  the  brakes  ?    b.  Suppose  the  car 
to  have  been  stopped  in  the  space  of  40  ft.  ,  what  was  the  average  force 
applied  ? 

79.  Activity.  —  The  activity  (sometimes  called  the  power)  of 
an  agent  is  the  rate  at  which  it  does  or  can  do  work  ;  or  it  is 
the  quantity  of  work  it  does  in  a  unit  of  time)  and  is  deter- 
mined by  the  formula 

W  (work) 


In  estimating  the  total  quantity  of  work  done,  the  time 
consumed  is  not  taken  into  consideration.     The  work  done  by 


96  MOLAR    DYNAMICS. 

a  hod-carrier  in  carrying  1000  bricks  to  the  top  of  a  building 
is  the  same  whether  he  does  it  in  a  day  or  a  week.  But  in 
estimating  activity,  as  of  a  man,  a  horse,  or  a  steam-engine, 
in  other  words,  the  rate  at  which  the  agent  is  capable  of  doing 
work,  it  is  evident  that  time  is  an  important  element.  The 
work  done  by  a  horse  in  raising  a  barrel  of  flour  20  feet  is 
about  4000  foot-pounds ;  but  even  a  mouse  could  do  the  same 
quantity  of  work  in  time. 

The  unit  in  which  activity  or  rate  of  doing  work  is  estimated 
is  called  (inappropriately)  a  horse-power.  A  horse-power  is 
550  foot-pounds  per  second,  33,000  foot-pounds  per  minute, 
or  1,980,000  foot-pounds  per  hour. 

The  logical  unit  of  activity  is  a  unit  of  work  in  a  unit  of 
time,  as  one  erg  per  second.  The  absolute  unit  of  activity, 
chiefly  used  in  measuring  electrical  activity,  is  the  watt,  or 
ten  million  ergs  per  second.  A  moderate  estimate  of  man's 
activity  is  100  watts. 

1  erg  per  second  =.=  .0000001  watt, 

1  horse-power  =r=  746  watts, 

1  foot-pound  per  minute  =c=  226,043  ergs  per  second. 

Activity  being  measured  by  the  numeric  of  the  work  done  per 
unit  of  time,  its  dimensional  equation  is  therefore  [A]  =  [WT-1] 

=  [ML2T-8]. 


Questions  and  Problems. 

1.  For  which  is  a  truck-horse  valued,  his  energy  or  his  activity  ? 

2.  Do  we  speak  of  the  activity  or  the  energy  of  a  steam-engine  ? 

3.  Which  do  we  apply  to  levers  and  machines  in  general,  power  or 
force  ? 

4.  "  Energy  is  the  power  of  doing  work."     Is  this  true  ? 

5.  Shall  we  say  that  the  activity,  or  the  energy,  of  the  horse  is  greater 
than  that  of  man  ? 

6.  How  much  work  can  a  2  horse-power  engine  do  in  an  hour  ? 


ACTIVITY.     '  97 

7.  a.    What  quantity  of  work  is  required  to  raise  50  tons  of  coal  from 
a  mine  200  feet  deep  '?     b.  An  engine  of  how  many  horse-power  would  be 
required  to  do  it  in  two  hours  ? 

8.  A  car  of  mass  6000  k  is  drawn  by  a  horse  at  a  speed  of  100  in  per 
minute.     The  index  of  the  dynamometer  to  which  the  horse  is  attached 
stands  at  40  K.    a.  At  what  rate  is  the  horse  working  ?     b.  Express  the 
rate  in  horse-power. 

0.  A  dynamometer  shows  that  a  span  of  horses  pull  a  plow  with  a 
constant  force  of  70  K.  What  activity  is  required  to  work  the  plow  if  they 
travel  at  the  rate  of  3  km  per  hour  ? 

10.  What  horse-power  in  an  engine  will  raise  1, 350,000  K  5m  in  an 
hour  ? 

11.  How  long  will  it  take  a  3  horse-power  engine  to  raise  10  tons 
50  feet  ? 

12.  How  far  will  a  2  horse-power  engine  raise  1000  K  in  10  seconds  ? 

13.  A  force  of  10,000  dynes  acting  through  a  space  of  100  meters  per 
second  furnishes  an  activity  of  how  many  watts  ? 

14.  The  wind  moves  a  vessel  with  a  uniform  velocity  of  5  miles  an 
hour  against  a  constant  resistance  of  2000  pounds.      What  activity  is 
furnished  by  the  wind  ? 

-   15.    If  a  2  horse-power  engine  can  just  throw  1056  pounds  of  water  to 
the  top  of  a  steeple  in  two  minutes,  what  is  the  hight  of  the  steeple  ? 

16.  A  cannon  ball  of  10,000  g  is  discharged  with  a  velocity  of  45,000  cm 
per  second.     Find  its  kinetic  energy.  Ans.  10125  X  109  ergs. 

17.  In  the  last  question,  find  the  mean  force  exerted  upon  the  ball  by 
the  powder,  the  length  of  the  barrel  being  200  cm. 

Ans.  50625  X  106  dynes. 

18.  Supply  the  following  ellipses  by  selecting  appropriate  words  from 
the  following :  viz.  force,  work,  energy,  activity.     When  —  acts  through 
space  —  is  performed,  and  —  is  imparted.     The  rate  at  which  —  is  per- 
formed determines  the  —  of  the  agent.     The  —  of  a  bullet  flying  through 
vacant  space.     The  —  of  a  horse.     The  —  of  wind.     The  —  of  a  bent 
bow.     What  —  must  a  bullet  of  mass  1  ounce  have  that  it  may  rise  4 
seconds  ?     What  —  is  consumed  by  a  steamer  in  crossing  the  ocean  ? 
What  —  is  necessary  that  it  may  traverse  300  knots  per  day,  and  what 
must  be  the  average  —  exerted  to  overcome  the  resistances  at  the  required 
rate? 


98 


MOLAR    DYNAMICS. 


SECTION  XI. 


MACHINES. 

80.    Uses  of  machines. 

Experiment  1.  —  Suspend,   as  in  Fig.  59,  a  fixed  pulley,  A,  and  a 

movable  pulley,  B.  Let  the  scale-pan 
C  counterbalance  the  pulley  B,  so  that 
there  will  be  equilibrium.  Suspend  from 
B  two  balls,  LL,  of  equal  weight,  and 
suspend  on  the  side  where  the  pan  is, 
a  single  ball,  K,  equal  to  one  of  the 
former.  The  single  ball  supports  the 
two  balls;  i.e.  by  the  use  of  the  machine, 
a  force  of  1  is  enabled  to  balance  a  force 
of  2.  So  far  no  work  is  done.  Place  a 
very  small  weight  in  the  pan ;  the  balls 
LL  rise,  and  work  is  done. 

As  the  weight  K  plus  a  very  small 
weight  causes  the  motion,  we  shall 
regard  this  as  the  force  (/) ;  and  as  the 
weights  LL  are  the  bodies  moved  (the 
pulleys  and  pan  being  parts  of  the 
machine  may  be  disregarded),  they  may 
be  regarded  as  the  resistance  (r)  over- 
come, or  the  body  on  which  work  is 
done.  Measure  the  respective  distances  through  which  /  acts  and  r  moves 
during  the  same  time,  r  moves  only  one-half  as  great  a  distance  as  that 
through  which  /  acts;  i.e.  if  r  rise  2  feet,  /  must  act  through  4  feet. 
Suppose  that  r  is  2  pounds,  then  /  is  1  +  pounds.  Now  2  (pounds)  X  2 
(feet)  =  4  foot-pounds  of  work  done  on  r.  Again,  1  +  (pounds)  X  4  (feet) 
=  a  little  more  than  4  foot-pounds  of  work  (or  energy)  expended. 

It  thus  seems  that,  although  a  machine  will  enable  a  small 
force  to  balance  a  large  force,  when  work  is  performed  the 
work  applied  to  the  machine  is  greater,  rather  than  less,  than 
the  work  which  the  machine  transmits  to  the  resistance.  The 
work  applied  is  greater  than  the  work  transmitted  by  the 
amount  of  work  wasted  in  consequence  of  friction  and  other 


FIG.  59. 


USE    OF    MACHINES.  99 

resistances.     So  that  by  the  employment  of  a  machine  nothing 
is  gained  in  work,  but  something  is  always  lost. 

What,  then,  is  the  advantage  gained  in  using  this  machine  ? 
Suppose  that  r  is  400  pounds,  and  that  the  utmost  force  that 
a  man  can  exert  is  a  little  more  than  200  pounds.  Then 
without  the  machine  the  services  of  two  men  would  be  required 
to  move  the  resistance ;  whereas  one  man  can  move  it  with  a 
machine,  but  he  will  be  obliged  to  move  twice  as  far  as  the 
resistance  moves,  a  matter  of  little  consequence  in  comparison 
with  the  advantage  of  being  able  to  do  the  work  alone.  The 
advantage  gained  in  this  instance  seems  to  be  one  of  convenience. 
Men,  however,  are  accustomed  to  speak  of  it  as  "a  gain  of 
force "  (or  more  commonly  and  inaccurately,  "of  power"), 
inasmuch  as  a  small  force  overcomes  a  large  resistance. 

Experiment  2.  —  If  instead  of  applying  the  small  additional  weight  to 
the  pa.n,  it  be  suspended  from  one  of  the  balls  LL,  the  weight  of  these 
balls,  together  with  the  additional  weight,  becomes  the  cause  of  motion, 
and  K  is  the  resistance.  In  this  case  there  is  a  loss  of  force,  because  the 
force  employed  is  greater  than  the  force  overcome.  Measure  the  dis- 
tances traversed  respectively  by  K  and  LL  in  the  same  time.  K  moves 
twice  as  far  as  LL,  and  of  course  with  twice  the  speed.  There  is  a  gain 
of  speed  at  the  expense  of  force. 

It  thus  appears  that,  if  it  should  be  desirable  to  move  a 
resistance  with  greater  speed  than  it  is  possible  or  con- 
venient for  the  force  to  act,  it  may  be  accomplished  through 
the  mediation  of  a  machine,  by  applying  to  it  a  force  propor- 
tionately greater  than  the  resistance.  This  apparatus  is  one 
of  many  contrivances  called  machines,  through  the  mediation  of 
which  force  can  be  applied  to  resistance  more  advantageously 
than  when  it  is  applied  directly  to  the  resistance. 

At  present  we  deal  with  machines  employed  as  means  for 
transmitting  and  modifying  motion  and  force.  Later  we  shall 
consider  machines  whose  function  is  to  transform  energy,  such 
as  the  steam  engine,  dynamo,  etc. 


100 


MOLAR    DYNAMICS. 


Some  of  the   many   advantages   derived  from  the  use  of 
machines  are : 

(1)  They  may  enable  us  to  exchange  intensity  of  force  for 
speed,  or  speed  for  intensity  of  force.     A  gain  of  intensity  of 
force  or  a  gain  of  speed  is  called  a  mechanical  advantage. 

(2)  They  may  enable  us  to   employ  a  force  in  a  direction 
that  is  more  convenient  than  the  direction  in  which  the  resis- 
tance is  to  be  moved. 

(3)  They  may  enable  us  to  employ  other  forces 
than  our  own  muscular  force  in  doing  work; 
e.g.  the  muscular  force  of  animals  ;  the  forces 
of  wind,  water,  steam,  etc. 

How  are  the  last  two  uses  illustrated  in 
Fig.  60?  The  pulleys  employed  are  called 
fixed  pulleys,  i.e.  they  have  no  motion  except 
that  of  rotation.  Is  any  mechanical  advantage 
gained  by  fixed  pulleys?  What  is  the  use  of  a 
fixed  pulley?  Pulley  B  (Fig.  59)  is  a  movable 
pulley.  What  advantage  is  gained  by  means  of 
a  movable  pulley  ? 

81.  General  law  of  machines.  — 
From  the  experiments  and  discussion 
above  we  derive  the  following  for- 
mula for  machines  : 

f*  =  rs'+w,  (1) 

in  which  /  represents  the  force  applied,  and  s  the  distance 
through  which  /  acts ;  r  represents  the  resistance  overcome, 
and  s'  the  distance  through  which  its  point  of  application  is 
moved ;  w  represents  the  wasted  work.  A  machine  in  which 
there  is  no  wasted  work  is  a  perfect  machine.  Such  a  machine 
is  purely  ideal,  as  none  exists.  If  in  our  calculations  we 
regard  a  machine  as  perfect  (though  subsequently  suitable 
allowance  must  be  made  for  the  wasted  work),  then  our 
formula  becomes  fs  =  rs',  (2) 


FIG.  60. 


GENERAL   LAW    OF    MACHINES.  101 

whence  r  :  f:  :  s  :  s' ;  i.e.  the  force  and  resistance  vary  inversely 
as  the  distances  which  their  respective  points  of  application  move. 
In  other  words,  the  ratio  of  the  resistance  to  the  force  is  the 
reciprocal  of  the  ratio  of  the  distances  which  these  points 
move  ;  thus,  if 

r  :  f=  4,  then  s'  :  s  =  £. 

This  law  applies  to  machines  of  every  description ;  hence  it  is 
called  the  General  or  Universal  Law  of  Machines.  When  r 
is  greater  than  f,  there  is  a  gain  of  intensity  of  force,  and 

=  the  ratio  of  gain  of  intensity  of  force.     When  s'  is  greater 

J 

s' 
than  s,  there  is  a  gain  of  speed,  and  -  =  the  ratio  of  gain  of 

*      **  f< 

speed.  \  ,•  ;  '•:  :    '."  • 

Since  fs,  the  work  done  upon  a  machine,;  is,  always  greater 
than  rs',  the  work  transmitted  by  "thie  machine1; 'we0  infer' that 
no  machine  creates  or  increases  energy.  No  machine  transmits 
more  energy  than  it  receives.  A  machine  may  enable  us  to 
gain  intensity  of  force,  but  not  energy.  By  taking  s  great 
enough,  f  can  be  made  as  small  as  we  please  ;  in  this  case  in 
proportion  as  force  is  gained,  time,  distance,  or  speed  is  lost. 

Formula  (1)  exhibits  the  relation  between  the  work  performed 
upon  the  machine  and  the  entire  work  transmitted  and  transformed 
by  the  machine.  But  at  any  given  instant  while  the  machine  is 
in  operation,  it  is  evident  that  (see  p.  91) 

fs  =  i  mv2  +  rs'  +  w.  (3) 

In  formula  (3)  |  ?nv2  represents  the  kinetic  energy  of  the  moving 
parts  of  the  machine. 

82.  Efficiency  of  machines.  —  The  efficiency  of  a  machine  is 
a  fraction,  usually  a  per  cent,  expressing  the  ratio  of  the 
energy  given  out  by  the  machine  and  utilized  to  the  total 
energy  expended  upon  the  machine.  The  limit  of  the  efficiency 
of  a  machine  is  unity,  which  is  the  efficiency  of  an  "  ideal," 


102  MOLAR    DYNAMICS. 

or  perfect,  machine,  in  which  no  energy  is  lost.  The  object 
of  improvements  in  machines  is  to  bring  their  efficiency  as 
near  to  unity  as  possible.  For  instance,  if  50  foot-pounds  of 
energy  be  expended  on  a  machine,  and  friction  convert  8  foot- 
pounds into  heat  and  5  foot-pounds  be  lost  in  consequence  of 
only  a  component  of  the  working  force  being  utilized,  so  that 
the  machine  is  able  to  give  out  only  37  foot-pounds,  its 
efficiency  is  f  £  =  74  per  cent.  If  the  friction  can  be  reduced 
one  half  and  an  improvement  can  be  made  in  the  machine 
which  will  render  the  entire  working  force  effective,  then 
there  will  be  wasted  only  4  foot-pounds  of  energy,  and  its 
efficiency  will  be  raised  to  f  §  =  92  per  cent.,  and  the  quantity 
of  work  which  the  machine  will  accomplish  will  be  increased 
in  the  ratio  of  92  :  74.. 

83.  Mechanical  powers. —  Machines,  however  complicated 
or  opii'pl££,''  are  largely  .composed  of  a  few  simple  machines 
long  known  as  the  ^ mechanical  powers."     As  usually  given 
they  are  the  Lever,  Wheel  and  Axle,  Inclined  Plane,  Wedge, 
Screw,  Pulley,  and  Knee. 

84.  Experiments  ivith  the  lever. 

Experiment  3.  —  Support  a  lever,  as  in  Fig.  61,  so  that  there  shall  be 
unequal  arms.  Move  W  until  the  lever  is  balanced  in  a  horizontal  posi- 
tion. Suspend  (say)  seven  balls  from  the  short  arm  (say)  one  space 

from  the  fulcrum.  Then  from 
the  other  arm  suspend  a  single 

(i  W/  <|>    v    "   ball  from  such  a  place  (in  this 

case  seven  equal  spaces  from  the 
fulcrum)  that  it  will  balance  the 
seven  balls.  There  is  now  equili- 

FlG  61  brium   between  the  two  forces. 

Suppose  the  smaller  force  to  be 

increased  a  little  and  to  produce  motion ;  what  mechanical  advantage 
(i.e.  intensity  of  force  or  speed)  would  be  gained  by  the  use  of  the 
machine  ?  What  is  the  ratio  of  gain,  the  small  additional  force  being 
neglected  ?  How  does  this  ratio  compare  with  the  ratio  between  the 
length  of  the  two  arms  ?  For  convenience  we  call  the  distance  of  the 


EXPERIMENTS    WITH    THE    LEVER. 


103 


point  of  application  of  the  force  from  the  fulcrum  the  force-arm,  and  the 
distance  of  the  resistance  from  the  fulcrum  the  resistance-arm. 

Suppose  the  small  additional  force  to  be  applied  to  the  short  arm  ; 
what  mechanical  advantage  would  be  gained  ?  What  would  be  the 
ratio  of  gain  ? 

While  the  general  law  of  machines  (p.  100)  is  always 
applicable,  its  application  is  not  always  convenient,  since,  for 
example,  it  necessitates  putting  the  machine  in  motion  in 
order  to  measure  s  and  s1 
(the  distances  traversed 
respectively  by  the  points 
of  application  of  the  force 
and  resistance  in  the  same 
time),  an  operation  which 
would  be  very  difficult 
and  tedious  in  many 
cases.  Hence,  a  special 
law,  one  in  which  the 
relation  between  the  ratio 
of  gain  and  the  ratio  be- 
tween certain  dimensions 
of  the  machine  is  stated, 
is  often  more  convenient 
in  practice.  For  example, 
in  our  experiment  with 
the  lever  we  discover  that 
B  :  F  :  :  force-arm:  resistance-arm,  i.e.  the  force  and  resistance 
vary  inversely  as  the  lengths  of  their  respective  arms.  Compare 
this  special  law  with  the  general  law.  Place  the  fulcrum  at 
other  points  in  the  lever,  and  thereby  vary  the  length  of  the 
arms,  and  verify  by  numerous  experiments  the  special  law 
of  levers. 


FIG.  62. 


Experiment  4.  —  By  means  of  a  pulley,  D,  so  arrange  (Fig.  62)  that 
both  F  and  R  may  be  on  the  same  side  of  the  fulcrum.     First,  place  in 


104 


MOLAR    DYNAMICS. 


the  pan  weights  sufficient  to  produce  equilibrium  in  the  machine  (for 
example,  in  this  case,  one  ball).  Then  suspend  weights  at  some  point,  as 
A,  and  place  other  weights  in  the  pan  to  counterbalance  these.  Verify 
the  law  of  levers.  If  A  be  the  resistance,  what  mechanical  advantage  is 
gained  ?  What  is  the  ratio  of  gain  ?  If  B  be  the  resistance,  what 
mechanical  advantage  is  gained  ? 

85.    Wheel  and  axle.  —  The  wheel  and  axle  consists  of  two 
cylinders  having  a  common  axis,  the  larger  of  which  is  called 


FIG.  63. 


FIG.  64. 


the  wheel,  and  the  smaller  the  axle,  as  A  and  C  (Fig.  63). 
The  wheel  may  be  moved  by  the  hand  or  by  a  string  with  a 
weight  attached  to  it. 

The  wheel  is  often  replaced  by  a  crank,  as  in  the  windlass, 
or  by  a  spoke,  as  in  the  capstan,  and  is  thus  employed  in 
hoisting  apparatus,  such  as  cranes,  derricks,  etc. 

The  wheel  and  axle  viewed  in  section  will  be  seen  (Fig.  64) 
to  be  only  a  modification  of  the  lever  which,  unlike  the  latter, 
may  be  continuous  in  its  operation.  C  is  the  fulcrum,  the 
radius  CA.  is  the  force-arm,  and  the  radius  OB  the  resistance- 


INCLINED    PLANE.  105 

arm.  The  laws  pertaining  to  this  machine  are  virtually  the 
same  as  those  of  the  lever.  For  example,  when  the  force  f  is 
applied  to  the  wheel  and  the  resistance  r  is  at  the  axle, 

r= 


R  (radius  of  wheel)  '  R'  (radius  of  axle) 
1  1 


C  (circumference  of  wheel)  '  C"  (circumference  of  axle). 

86.  Inclined  plane.  —  Any  plane  surface  not  horizontal  or 
vertical,  known  as  an  inclined  plane,  may  be  used  as  a  simple 
machine  for  gaining  intensity  of  force;  e.g.  a  plank  resting 
with  one  end  on  a  cart  body  and  the  other  on  the  ground,  a 
hill-side,  or  a  road-grade.  The  gradient  is  the  quantity  of  rise 
per  horizontal  foot,  or  it  is  the  ratio  of  the  vertical  rise  to  the 
horizontal  distance. 

When  a  body  is  pressed  against  a  hard,  smooth  surface,  the 
resistance  offered  by  the  surface  is  at  right  angles  to  the 
surface.  A  body,  e.g.  a  sphere,  may  be  supported  on  a 
horizontal  surface,  for  the  weight  acting  downward  is  counter- 
acted by  the  upward  reaction  of  the  plane.  But  since  on  an 
inclined  plane  the  reaction  is  not  vertically  upward,  a  body 
cannot  rest  on  it  without  the  aid  of  another  force. 

The  mechanical  advantage  of  this  machine  depends  on  the 
principle  of  the  resolution  of  a  force  into  its  components.  Let 

T)  /^1 

AB  (Fig.  65)  be  an  inclined  plane  whose  gradient  is  —r^m  Let 

A  (_/ 

a  be  the  centroid  of  the  weight  W  (technically  called  the  load). 
The  line  of  direction  of  the  load  is  along  the  vertical  ao,  but 
the  pressure  exerted  upon  the  plane  is  in  the  direction  ac,  and 
the  reaction  of  the  plane  is  in  the  direction  ca.  We  may  take 
any  length  along  the  vertical  as  ab  to  represent  the  load  W. 
Draw  be  parallel  to  AB  to  meet  ac.  Complete  the  paral- 
lelogram adbc  with  ab  as  its  diagonal.  The  force  ab  is 
thereby  resolved  into  two  forces,  ac  representing  the  pressure 


106 


MOLAR    DYNAMICS. 


upon  the  plane,  and  ad  representing  an  unbalanced  force 
tending  to  move  W  along  the  plane  B  A.  It  is  evident  that 
to  produce  equilibrium,  i.e.  to  support  the  body  on  the  plane 
AB,  a  force  equal  to  ad,  but  opposite  in  direction,  must  be 


FIG.  65. 


ill' 


employed.  Now  it  may  be  proved  geometrically  that  the 
triangles  adb  and  BCA  are  similar;  i.e. 

da:  ab  :  :  CB  :  BA. 

But  da  represents  the  force /necessary  to  produce  equilibrium, 
while  ab  represents  the  load  or  resistance  r;  CB  represents 
the  hight  h,  and  BA  the  length  Z,  of  the  inclined  plane. 
Therefore 

f'.r-.-.h'.l,  orf=jr. 

Hence  a  given  force  acting  parallel  with  the  direction  of 
inclination  of  an  inclined  plane,  will  support  a  weight  as  many 
times  greater  than  itself  as  the  length  of  the  inclined  plane  is 
greater  than  its  vertical  hight.  Corollary :  with  a  given  length 
of  inclined  plane  the  greater  its  vertical  hight,  i.e.  the  steeper 
it  is,  the  greater  f  must  be. 


ANGLE    OF    REPOSE. 


107 


Suppose  that  a  (Fig.  65),  the  point  of  application  of  r,  be 
moved  to  b',  how  high  is  the  load  raised?  Through  what 
distance  does  /  act  ?  Show  that  the  general  law  of  machines 
is  applicable  to  this  case. 

87.  Angle  of  repose. 

When  work  is  done,  i.e.  when  the  load  is  moved  up  the  inclined 
plane,  a  force  greater  than  /  must  be  employed,  partly  to  overcome 
friction,  and  partly  to  produce  acceleration.  On  the  other  hand,  if 
a  body  be  allowed  to  roll  or  slide  down  an  inclined  plane,  the  force 
of  gravitation  overcomes  friction  and  produces  acceleration.  Since  / 
diminishes  with  the  angle  of  inclination  of  the  plane,  there  must  be 
an  angle  at  which  /  will  be  just  equal  to  the  friction.  This  angle  is 
called  the  angle  of  repose.  If  the  angle  of  inclination  be  greater 
than  the  angle  of  repose,  the  body  is  acted  on  by  an  unbalanced 
force  whose  magnitude  is  determined  by  the  inclination  of  the  plane, 
and  the  acceleration  produced  thereby  will  be  proportional  to  the 
unbalanced  force.  This  suggests  a  way  of  "  diluting  "  the  action  of 
gravity,  so  as  to  be  able  to  study  the  effects  of  a  constant  unbalanced 
force,  and  a  marble  rolling  down  a  smooth  plane  very  slightly 
inclined  furnishes  a  very  simple  substitute  for  the  falling  weights 
in  Atwood's  Machine. 

88.  The  wedge  is  a  triangular  prism,  used  commonly  as  a 
movable  inclined  plane  for  moving  great  resist-  ^ 

ances  through  short  distances.  It  usually 
consists  of  two  inclined  planes  as  AcP  and  n"n 
BcP  (Fig.  66).  The  force  applied  acts  in  the 
direction  po  and  the  resistance  acts  at  right 
angles  to  the  planes,  or  in  the  directions  Dm 
and  En.  The  force  applied  is  of  the  nature 
of  a  percussion,  as  that  of  a  sledge  ;  besides, 
friction  and  other  resistances  form  so  con- 
siderable a  factor  in  its  use  that  no  definite 
law  of  any  practical  value  can  be  given, 
further  than  that,  with  a  given  thickness.  FIG.  66. 

the  longer  the  wedge  the    greater  the  gain  in  intensity  of 
force. 


108 


MOLAR    DYNAMICS. 


89.  The  screw  is  another  variety  of  the  inclined  plane,  as 
may  be  shown  by  winding  a  triangular  piece  of  paper  around 
a  cylinder,  e.g.  a  lead  pencil  (Fig.  67).  The  hypotenuse  will 


FIG.  67. 


FIG.  G8. 


form  a  spiral  about  the  cylinder  resembling  the  threads  of 
a  screw. 

In  actual  practice  the  screw  consists  of  two  parts  :   (1)  a 
convex  grooved  cylinder,  or  screw,  S  (Fig.  68),  which  turns 
within  (2)  a  hollow  cylinder,  or  nut,  N.     The  concave  surface 
of  the  latter  is  cut  with  a  thread  corresponding 
to  the  thread  of  the  screw.     The  force  is  em- 
ployed either  to  turn  the  screw  within  an  immov- 
able nut,  or  to  turn  the  nut  about  a  fixed  screw. 
In  either  case  the  force  is  usually  applied  to  a 
lever  or  wheel  fitted  either  to  the  screw  or  to 
the  nut. 

During  a  single  rotation  of  the  screw  or  nut, 
the  load  or  resistance  is  moved  a  distance  equal 
to  the  vertical  distance  between  the  correspond- 
ing surfaces  of  two   successive  threads,  usually  termed  the 


a—  *- 


Fro.  69. 


THE    KNEE    OK    TOGGLE-JOINT. 


109 


FIG.  70. 


pitch  of  the  screw,  as  ab  (Fig.  69).  Then  in  conformity  to 
the  universal  law  of  machines  the  force  is  to  the  resistance  as 
the  distance  between  the  corresponding  surfaces  of  two  successive 
threads  is  to  the  circumference  of  the  circle  described  by  the 
force. 

Since  a  screw  turning  in  a  nut  advances  only  its  pitch  distance  at 
each  revolution,  a  finely  cut 
screw  furnishes  an  instru- 
ment well  adapted  to  meas- 
ure very  minute  distances. 
For  example,  if  the  screw  C 
of  the  micrometer  caliper 
(Fig.  70)  have  a  pitch  of  one 
millimeter,  and  the  thimble 
1)  be  divided  near  its  end  A 
into  one  hundred  parts  so  as 
to  register  hundredths  of  a 
revolution,  it  is  evident  that  any  object  (e.g.  a  hair)  placed  in  its 
jaws  at  B  can  be  measured  to  the  hundredth  of  a  millimeter. 

90.  The  knee  or  toggle-joint.  —  This  machine  also  is  em- 
ployed where  great  pressure  has 
to  be  exerted  through  a  small 
space,  as  in  punching  and  shear- 
ing iron.  Force  applied  at  C 
(Fig.  71)  in  the  direction  CD 
will  cause  the  jointed  bars  to  be 
brought  into  line  with  each  other 
and  tend  to  push  the  objects  at 
the  other  extremities  of  the  bars 
apart.  The  nearer  these  bars 
approach  to  a  straight  line,  the 
HI  greater  pressure  will  a  given 
FIG.  71.  force  produce. 


110 


MOLAR    DYNAMICS. 


Exercises. 

1.  a.  When  is  a  machine  said  to  gain  intensity  of  force  ?    b.  When 
is  it  said  to  gain  speed  ? 

2.  a.  How  is  intensity  of  force  gained  by  the  use  of  a  machine  ? 
6.  How  is  speed  gained  by  the  use  of  a  machine  ? 

3.  a.  What  is  mechanical  advantage  ?     b.  Give  a  rule  by  which  the 


FIG.  72. 


mechanical  advantage  that  may  be  gained  by  any  machine  may  be 
calculated. 

4.  Energy  is  applied  to  a  machine  at  the  rate  of  250  ft.  Ibs.  per  minute 
and  it  transmits  200  ft.  Ibs.  per  minute.     What  is  its  efficiency  ? 

5.  Fig.  72  represents  a  pile-driver,     a.  How  can  the  energy  or  the 
work  which  the  weight  W  can  do  when  it  is  raised  a  given  distance  be 
computed  ?    6,  What  benefit  is  derived  from  the  use  of  the  machine  in 


EXERCISES. 


Ill 


raising  the  weight  ?  c.  Suggest  some  simple  attachment  to  the  machine 
which  would  enable  one  man  to  raise  the  weight,  d.  Suggest  some 
attachment  by  means  of  which  a  horse  could  be  employed  to  do  the 
work.  e.  What  difference  will  it  make  whether  the  weight  is  raised 


FIG.  73. 

5  feet  or  10  feet  ?    /.  Illustrate,  by  means  of  this  machine,  what  you 
understand  by  force  and  energy. 

6.  a.  What  advantage  is  gained  by  a  nut-cracker  (Fig.  73)  ?    b.  What 
is  the  ratio  of  gain  ? 

7.  a.  What  advantage  is  gained  by  cutting  far  back  on  the  blades  of 
shears  near  the  fulcrum  (Fig.  74)  ?     Why  ?     6.  Should  shears  for  cutting 


FIG.  74. 


metals  be  made  with  short  handles  and  long  blades,  or  the  reverse  ? 
c.  What  is  the  advantage  of  long  blades  ? 

8.  The  arm  is  raised  by  the  contraction   (shortening  by  muscular 
force)    of    the    muscle   A    (Fig.  75), 

which  is  attached  at  one  extremity 
to  the  shoulder  and  at  the  other  ex- 
tremity B  to  the  fore-arm,  near  the 
elbow,  a.  When  the  arm  is  used,  as 
represented  in  the  figure,  to  raise  a 
weight,  what  kind  of  machine  is  it  ? 
6.  What  mechanical  advantage  is 
gained  by  it  ?  c.  How  can  the  ratio 
of  gain  be  computed  ?  d.  For  which 
purpose  is  the  arm  adapted,  to  gain 
intensity  of  force  or  speed  ? 

9.  Is  work  done  when  the  moment  of  the  force  applied  to  a  lever  is 
equal  to  the  moment  of  the  resistance  ?     Why  ? 


FIG.  75. 


112 


MOLAR    DYNAMICS. 


B 


FIG.  76. 


!  A  10.  If  F  (Fig.  76)  be  the  fulcrum  of 
the  lever  C  A,  and  AB  represent,  on  a 
scale  of  1  cm  =  1  k,  a  force  applied  at  A, 
what  force  applied  at  C  in  the  direction 
C  D  will  produce  equilibrium  ? 

11.    With  a  wheel  and  axle  a  force 

of  8  Ibs.  sustains  a  weight  of  56  Ibs. ;  what  is  the  ratio  between  the  radii 
of  the  wheel  and  of  its  axle  ? 

12.  A  capstan  turned  by  two  horses  is  used  to  draw  a  boat ;  the  horses 
are  attached  to  the  levers  12  feet 

from  the  axis  of  the  capstan  ;  the 
radius  of  the  axle  is  18  in.  When 
each  horse  pulls  with  a  force  of 
1,000  Ibs.  what  force  is  exerted 
upon  the  boat  ? 

13.  Suppose   the  screw  in  the 
letter-press  (Fig.  77)  to  advance  £ 
inch  at  each  revolution,  and  a  force 
of  25  pounds  to  be  applied  to  the  cir- 
cumference of  the  wheel  6,  whose 
diameter  is  14  inches.     What  pres- 
sure would  be  exerted  on  articles 
placed  beneath  the  screw  ? 

14.  A  lever  is  75  cm  long  ;  where  must  the  fulcrum  be  placed  in  order 
that  a  force  of  2  k  at  one  end  may  balance  4  k  at  the  other  end  ?    What 
will  be  the  pressure  on  the  prop  ? 


FIG.  77. 


FIG.  78. 

15.  Two  weights,  of  5  k  and  20  k,  are  suspended  from  the  ends  of  a 
lever  70cm  long.  Where  must  the  fulcrum  be  placed  that  they  may 
balance  ? 


EXERCISES.  113 

16.  If  P  (Fig.  78),  weighing  lib.,  is  suspended  15  spaces  from  the 
fulcrum  of  the  steelyard,  what  weight  (W)  suspended  3  similar  spaces  the 
other  side  of  the  fulcrum  will  balance  it  ? 

17.  How  would  you  weigh  out  6  pounds  of  tea  with  the  same  steel- 
yard ? 

18.  a.  A  skid  12  feet  long  rests  with  one  end  on  a  cart  at  a  hight  of 
3  feet  from  the  ground.     What  force  will  roll  a  barrel  of  flour  weighing 
200  Ibs.  over  the  skid  into  the  cart  ?     6.  What  amount  of  work  will  be 
required  ? 

19.  a.  Draw  a  line  to  represent  an  inclined  plane.     Find  what  is  the 
least  force  that  will  prevent  a  ball  weighing  96  Ibs.  from  rolling  down  the 
plane.     6.  Find  the  pressure  which  the  ball  will  exert  upon  the  plane. 

20.  An  iron  safe  on  trucks,  weighing  two  tons,   is  prevented  from 
rolling  down  an  inclined  plane  by  a  force  of  250  Ibs.     What  is  the  ratio 
of  the  length  of  the  plane  to  its  hight  ? 

21.  The  gradient  of  an  inclined  plane  is  1  ft.  in  4  ft.     To  produce 
equilibrium  on  this  plane  what  relation  must  the  force  applied  parallel 
with  the  plane  bear  to  the  load  ? 

22.  If  the  circumference  of 

an  axle  (Fig.  79)  be  60cm,  and          ,&-i——J^K^—*i^^3       /  \ 
the  force  applied  to  the  crank  =™» 

travel  240cm  during  each  revo- 
lution, what  force  will  be  neces- 
sary to  raise  a  bucket  of  coal 
weighing  40  k  ? 

23.  Through  how  many  me- 
ters must  the  force  act  to  raise 

the  bucket  from  a  cavity  10m  FlG 

deep? 

24.  The  truck  (Fig.  80)  is  a  lever  ;  the  fulcrum  is  at  the  axle  M  of  the 
wheels.     A  B  represents  the  line  of  direction  of  the  load,  i.e.  the  direction 
in  which  the  resistance  acts;  and  CD  represents  the  direction  in  which 
a  force  acts  to  produce  equilibrium  in  the  load  in  its  present  position, 
a.  What  represents  the  force-arm  ?     b.  What  represents  the  resistance- 
arm  ?     c.    The  force  required  to  support  the  load  is  what  part  of  the 
load  ?    d.  Would  greater,  or  less,  force  be  required  if  it  were  applied  at 
E  instead  of  C  ?     Why  ?     e.  How  may  the  load  be  supported  without  any 
force  applied  to  the  lever,  the  legs  not  touching  the  ground  ?    /.  Would 
its  equilibrium  in  this  position  be  stable  or  unstable  ?   Why  ?     g.  Suppose 
the  feet  F  to  rest  upon  the  ground,  how  would  the  pressure  of  the  load  be 
distributed  between  the  feet  and  wheels  ?     h.  Which  is  better  suited  for 


114 


MOLAR    DYNAMICS. 


moving  heavy  burdens,  a  wheelbarrow  or  a  truck  ?  Why  ?  i.  Suppose 
that  C  D  represents  the  supporting  force  and  C  G  the  force  employed  in 
moving  the  load,  how  would  the  intensity  and  direction  of  the  single 
force  that  accomplishes  both  results  be  found  ? 

25.    A  plank  12  feet  long  and  weighing  24  pounds  is  supported  by  two 


FIG.  80. 


props,  one  3  feet  from  one  end,  and  the  other  1  foot  from  the  other  end. 
What  is  the  pressure  on  each  prop  ? 

26.    What  must  be  the  diameter  of  a  wheel  in  order  that  a  force  of  20 


FIG.  81. 


FIG.  82. 


pounds  applied  at  its  circumference  may  be  in  equilibrium  with  a  resist- 
ance of  600  pounds  applied  to  its  axle,  which  is  3  inches  in  diameter  ? 

27.  How  would  you  calculate  the  mechanical  advantage  gained  by  a 
machine  like  that  of  Fig.  81  ?  (On  the  axle  A  is  an  endless  screw  a,  by 
means  of  which  motion  is  communicated  from  the  axle  to  the  wheel  W.1) 


COMBINATION    OF    MACHINES. 


115 


28.  a.  Where  is  the  fulcrum  in  a  claw-hammer  (Fig.  82)  ?    b.  What 
is  the  ratio  of  the  mechanical  advantage  gained  by  means  of  it  ? 

29.  In  its  technical  meaning,  a  "perpetual  motion  machine "  is  not  a 
machine  that  will  run  indefinitely,  but  a  machine  which  can  do  work 
indefinitely  without  the  expenditure  of  energy.     Show  that  such  a  machine 
is  impossible. 

SECTION  XII. 

COMBINATION    OF    MACHINES. 

91.  Combination  of  pulleys. — As  has  been  shown  (p.  98), 
mechanical  advantage  is  gained  with  the  movable  pulley.  In 
Fig.  83,  M,  the  cord  passing  around  the  movable  pulley  may 
be  supposed  to  be  divided  into  two  parts  each  supporting  half 

M  N 


FIG.  83. 


FIG.  84. 


the  load;  the  tension  in  each  part  is  half  the  load,  and  the 
supporting  force  P  is  half  the  load.  In  Fig.  83,  N,  the  movable 
block  A  contains  two  pulleys,  the  cord  supporting  the  load  is 
divided  into  four  parts,  and  P  is  one  fourth  of  L  ;  and  generally 
with  a  combination  of  pulleys  having  a  continuous  cord 


i.e.  the  force  is  equal  to  the  load  divided  by  the  number  of  parts 
of  the  cord  supporting  the  movable  block. 


116 


MOLAR    DYNAMICS. 


92.  Combination  of  levers.  —  In  the  arrangement  shown  in 
Fjg.  84  there  are  three  simple  levers  combined  so  as  to  form 
one  compound  lever.  The  supporting  force  is  applied  at  A  : 
the  resistance  applied  to  this  simple  lever  at  B  is  identical 
with  the  force  applied  at  A',  and  so  on.  Now 

Continuous  product  of  resistance-arms 
*  "  Continuous  product  of  force-arms 

A  combination  of  levers  similar  to  this  may  be  seen  in 
scales  used  for  weighing  very  heavy  bodies  such  as  the 
so-called  platform  "hay  scales,"  in  which  a  comparatively 
small  weight  counterbalances  the  heavy  load. 

93.  Combinations  of  the 
wheel  and  axle.  —  Fig.  85 
represents  a  train  of  wheels 
in  gear.  A  train  of  wheels 
being  analogous  to  a  com- 
pound lever,  the  mechanical 
advantage  gained  is  obvi- 
oiisly  the  ratio  of  the  con- 
tinued product  of  the  radii 
of  the  wheels  to  the  con- 
tinued product  of  the  radii 
of  the  axles. 


FIG.  85. 


Exercises. 


1.  When  there  are  four  movable  pulleys  in  one  block,  what  length  of 
cord  passes  through  the  hands  in  raising  a  weight  6  inches  ? 

2.  What  force  must  a  man  weighing  180  pounds  use,  to  support  him- 
self by  means  of  the  pulleys  in  Fig.  83,  N  ? 

3.  The  circumference  of  the  circle  described  by  the  end  of  the  lever  of 
a  screw  is  9  feet,  and  there  are  three  threads  to  the  inch  ;  what  pressure 
will  a  force  of  100  pounds  exert  ? 

4.  Suppose  the  lengths  of  the  arms  of  the  several  levers  in  Fig.  84 
bear  the  following  relations  to  each  other:  5:1,4:1,  and  3:1;  what  force 
applied  at  A  will  support  180  pounds  at  W  ? 


COMBINATION  OF  MACHINES. 


11? 


5.  a.  Of  how  many  and  what  simple  machines  does  the  crane  (Fig.  86) 
consist  ?  b.  How  would  you  calculate  the  mechanical  advantage  gained 
by  it? 


FIG.  86. 


6.    a.  In  what  sense  are  machines 
is  no  machine  labor-saving  ? 


labor-saving"?     6.  In  what  sense 


118  MOLAR    DYNAMICS 


CHAPTER  II. 

GRAVITATION,  OR  UNIVERSAL  ATTRACTION  BETWEEN 

MASSES. 

94.  Gravitation  is  universal.  —  An  unsupported  body  falls 
to  the  earth.     This  is  evidence  of  an  action  or  stress  between 
the  earth  and  the  body.     It  has  been  ascertained  by  careful 
observation  that  when  a  ball  is  suspended  by  a  long  string  by 
the  side  of  a  mountain,  the  string  is  deflected  from  the  vertical 
toward  the  mountain  in  consequence  of  an  attraction  between 
the  mountain  and  the  ball.     Delicate  experiments  show  that 
very  small  bodies  tend  to  approach  one  another,  and  that  the 
tendency  of  a  body  to  fall  to  the  earth  is  but  a  single  instance 
of  a  tendency  existing  in  all  kinds  and  quantities  of  matter. 

That  there  is  an  attraction  between  the  sun  and  the  earth, 
and  the  earth  and  the  moon,  is  shown  by  their  curvilinear 
motions.  Tides  and  tidal  currents  on  the  earth  are  due  to  the 
attraction  of  the  sun  and  the  moon.  This  attraction  which 
exists  between  all  masses  is  called  gravitation.  When  bodies 
under  its  influence  tend  to  approach  one  another,  they  are  said 
to  gravitate.  Since  this  attraction  ever  exists  between  all 
bodies,  at  all  distances,  it  is  called  universal  gravitation.  The 
theory  of  universal  gravitation  was  established  by  Newton. 
No  concept  in  science  rests  on  a  surer  foundation. 

95.  Weight.  —  The  attraction  between  the  earth  and  a  ter- 
restrial body  is  called  the  weight  of  that  body.     The  weight 
of  a  body,  therefore,  is  the  measure  of  the  force  of  attraction 
between  the  body  and  the  earth. 

We  do  not  know  the  cause  of  gravitation.  Whether  the 
seat  of  the  attraction  or  energy  is,  as  the  language  in  common 
use  indicates,  in  the  bodies  themselves,  or  whether  it  exists  in 


LAW    OF    GKAVITATION.  119 

some  medium,  which  we  may  suppose  to  surround  all  bodies 
and  fill  all  intervening  space,  we  do  not  know.1 

96.  Law  of  gravitation.  —  Methods  first  given  by  Newton 
in  the  Principia,  but  too  elaborate  for  our  purpose,  have 
established  the  fact  that  the  magnitude  of  the  attraction 
between  any  two  bodies  depends  upon  two  things,  their 
masses  and  the  distance  between  their  centroids.  The  Law  of 
Universal  Gravitation  is  as  follows  :  — 

The  attraction  between  every  two  bodies  of  matter  in  the 
universe  varies  directly  as  the  product  of  their  masses,  and 
inversely  as  the  square  of  the  distance  between  their  centroids.2 

Representing  the  masses  of  two  bodies  by  m  and  m',  the 
distance  between  their  centers  of  mass  by  d,  and  the  attrac- 
tion by  g,  this  relation  is  expressed  mathematically  thus  : 


g  oc    (varies  as)  —^-     For  example,  if  the  mass  of  either 

body  be  doubled,  the  product  (mm')  of  the  masses  is  doubled, 
and  consequently  the  attraction  is  doubled.     If  the  distance 


between   their   centers  of  mass  be  doubled,  then  (  — 


(2*  v 


the  attraction  becomes  one-fourth  as  great. 

97.  Galileo's  experiment.  —  Galileo  let  fall  from  the  top  of 
the  leaning  tower  at  Pisa  iron  balls  of  different  masses,  and 
found  that  they  fell  with  equal  acceleration  and  reached  the 
ground  at  the  same  instant.  This  celebrated  experiment 
established  two  important  facts  :  — 

(1)  At  any  given  place  the  acceleration  due  to  gravitation  is 
independent  of  the  mass  of  the  falling  body ;  in  other  words, 

1  "  It  may  turn  out  to  be  a  property  inherent  in  matter,  and  an  exception  to  every 
known  case  ;  but  it  is  more  probable  that  it  is  not  an  inherent  property  in  matter  at 
all,  but  a  property  due  to  a  strain  in  the  medium  in  which  all  matter  is  immersed." 
(LODGE.)    The  gravitation  stress  existing  in  this  medium  may  be,  in  some  respects, 
analogous  to  the  stress  which  exists  in  a  stretched  rubber  band,  which  would  tend  to 
bring  together  any  bodies  between  which  it  might  be  stretched. 

2  The  attraction  between  two  gram-masses  whose  centroids  are  one  centimeter 
apart  is  one  fifteen  millionth  of  a  dyne. 


120  MOLAR    DYNAMICS. 

for  all  bodies  at  the  same  place  the  acceleration  due  to  the 
earth's  attraction  is  the  same. 

Let  /  and  /'  be  the  intensities  of  two  attractive  forces 
acting  to  move  two  bodies,  whose  masses  are  respect- 
ively m  and  m',  to  the  earth  ;  then  (p.  40) 

•/'=  m  a,  and /' =  m' «' ; 
but,  as  proved  by  Galileo's  experiment, 


hence  (dividing)  ~-f- 

and,  in  general,  /oo  m, 

i.e.   (2)  the   intensity  of  the  earth's  attraction  at  the 

same  place  varies  as  the  mass. 

In  other  words,  the  deductions  from  this  expen- 
se. 87.     ment  are  .  ^  that  all   free  bodies,  whatever  their 
mass,  fall  toward  the    earth  with    equal   accelerations,   and 
(2)  that  if  one  body  possess  twice  the  mass  of  another,  twice 
the  force  is  required  to  give  it  the  same  acceleration. 

Proposition  (1)  is  seemingly  contradicted  by  every-day 
experience,  for  if  a  coin  and  a  piece  of  tissue  paper  be 
dropped  from  a  hight  they  fall  with  very  different  velocities 
and  accelerations.  But  if  a  coin  and  several  bits  of  paper 
be  placed  in  a  long  glass  tube  (Fig.  87),  the  air  exhausted, 
and  the  tube  turned  end  for  end,  it  will  be  found  that  the 
coin  and  the  papers  fall  in  the  vacuum  with  equal  velocities. 
It  is  evident,  then,  that  when  there  is  a  difference  in  the 
acceleration  of  falling  bodies  at  the  same  place  it  is  not  due 
to  the  force  of  gravitation  but  to  some  other  force,  e.n.  the 
resistance  of  the  air. 

98.     Variation  of  gravitation,  or  y,  on  the  earth's  surface.  — 
A  spherical  body  of  uniform  density  acts  upon  a  particle  out- 
side it  as  if  the  entire  mass  were  collected  at  its  center.     If 
the  earth  were  a  homogeneous  sphere  and  at  rest,  then  the 


WEIGHT    ABOVE    THE    EARTH'S    SURFACE.  121 

value  of  (j  would  be  constant  at  its  surface  since  every  point 
in  it  would  be  equidistant  from  the  center.  But  the  earth 
is  a  spheroid,  its  polar  diameter  being  about  43  kilometers 
(nearly  27  miles)  less  than  the  equatorial  diameter.  Conse- 
quently the  value  of  g  is  less  in  the  equatorial  than  in  the 
polar  regions,  i.e.  a  given  body  stretches  a  spring  balance  less 
as  it  is  carried  from  either  pole  toward  the  equator.  The  loss 
of  weight  of  any  body  due  to  this  increase  of  distance  from 
the  center  of  the  earth  in  being  transported  from  the  poles  to 
the  equator,  is  estimated  to  be  -g^-g  of  its  weight  at  the  poles. 
But  we  have  previously  seen  (p.  74)  that  the  centrifugal 
force  at  the  equator  diminishes  the  weight  of  a  body  ^J7. 
Xovv  in  consequence  of  difference  in  distance  from  the  center 
of  mass  of  the  earth  and  difference  in  velocity  due  to  the  earth's 
rotation,  a  body  weighs  at  the  equator  5^  +  ^^  =  T^  less 
than  at  the  poles. 

99.  Weight  above  the  earths  surface.  —  We  infer  from  the 
law  of  gravitation  that  a  body  weighs  more  at  the  earth's 
surface  than  above  it ;  in  other  words,  bodies  become  lighter 
as  they  are  raised  above  the  earth's  surface.     But  since  the 
force  diminishes  as  the  square  of  the  distance  from  the  center 
(not  from  the  surface)  of  the  earth,  and  as  the  surface  is  about 
4,000  miles  from  the  center,  the  diminution  for  a  few  miles  or 
for  any  distance  which  we  are  able  to  raise  bodies  is  scarcely 
perceptible  ;    hence  in  all  commercial  transactions  we  may, 
without  important  error,   buy  and  sell  as   if   the  weighing 
always  took  place  at  the  same  distance  from  the  center  of 
the  earth,   in  which   case    mass    is    strictly  proportional  to 
weight. 

100.  Wpitjht  below  the  earths  surface. 

It  may  be  demonstrated  geometrically  (Wood's  Elementary 
Mechanics,  p.  38,  Barker's  Physics,  p.  117)  that  if  a  particle  be 
placed  anywhere  within  a  homogeneous  hollow  spherical  shell  of 
matter,  as  at  ft,  c,  or  d  (Fig.  88),  it  is  in  a  state  of  equilibrium  in 


122  MOLAR   DYNAMICS. 

regard  to  the  attraction  of  the  matter  of  the  enveloping  shell,  i.e.  a 
body  thus  placed  within  a  hollow  shell  of  the  earth,  of  whatever 
thickness,  would  be  under  the  influence  of  balanced  forces  and 
hence  weightless.  Hence  if  a  body  be  taken  below  the  surface  of 
the  earth,  as  from  a  to  a'  (Fig.  89),  it  is  practically  placed  within  a 
hollow  spherical  shell  of  the  earth,  and  therefore  is  freed  virtually 


FIG.  88.  FIG.  89. 

from  the  gravitation  influence  of  this  shell.  Its  weight  is  now 
wholly  determined  by  the  gravitation  of  the  smaller  mass  mn.  So 
that  as  a  body  is  carried  below  the  surface  of  the  earth,  it  loses 
in  weight  as  much  as  it  would  if  it  were  being  transferred  to 
smaller  and  smaller  earths ;  consequently  at  the  earth's  center 
matter  is  under  the  influence  of  balanced  forces  and  hence  weight- 
less. If  the  earth  were  a  perfect  sphere  and  homogeneous,  the 
weight  of  a  body  would  diminish  uniformly  as  the  distance  from 
the  surface  increased. 

Exercises. 

1.  a.  Which  is  independent  of  mass,  weight  or  acceleration  ?    b.  Which 
varies  as  the  mass  ? 

2.  Why  does  a  hundred-pound  iron  ball  fall  with  no  greater  accelera- 
tion than  a  one-pound  ball  of  the  same  material  ? 

3.  a.  Which  falls  with  greater  acceleration  in  the  air,  an  iron  ball  or 
a  wax  ball  ?     Why  ?     b.  How  would  their  accelerations  compare  in  a 
vacuum  ?     c.  Is  acceleration  independent  of  kind  of  matter  ? 

4.  If  the  earth's  mass  were  doubled  without  any  change  of  volume, 
how  would  it  affect  your  weight  ? 

5.  On  what  principle  may  you  determine  that  the  mass  of  one  body  is 
ten  times  the  mass  of  another  body  ? 

6.  How  many  times  must  you  increase  the  distance  between  the  centers 
of  two  bodies  that  their  attraction  may  become  one-fourth  as  great  ? 


WEIGHT    BELOW    THE    EARTH'S    SURFACE. 


123 


7.  If  a  body  on  the  surface  of  the  earth  be  4,000  miles  from  the  cen- 
troid  of  the  earth,  and  weigh  at  this  place  100  pounds,  what  would  the 
same  body  weigh  if  it  were  taken  4,000  miles  above  the  earth's  surface  ? 

8.  The  masses  of  the  planets  Mercury,  Venus,  Earth,  and  Mars  are 
respectively  very  nearly  as  7,  79,  100,  and  12  ;  assuming  that  the  distance 
between  the  centers  of  the  first  two  is  the  same  as  the  distance  between 
the  centers  of  the  last  two,  how  would  the  attraction  between  the  first 
two  compare  with  the  attraction  between  the  last  two  ? 

9.  What  would  be  the  answer  to  the  last  question 
if  the  distance  between  the  centers  of  the  first  two 
were  four  times  the  distance  between  the  centers  of 
the  last  two  ? 

10.  Would  the  weight  of  a  soldier's  knapsack  be 
sensibly  less  if  it  were  carried  on  the  top  of  his  rifle  ? 

11.  If  you  hold  a  body  on  a  spring-balance  in  an 
elevator,  what  effect  will  be  noticed  as  you  start  to 
ascend?    What  effect,  as.  you  start  to  descend  ?    Ex- 
plain. 

12.  Let  E  (Fig.  90)  represent  the  earth  as  a  perfect 
homogeneous  sphere  of  a  radius  of  4,000  miles,    a.  If 
a  body  at  a  weigh  1  pound,  what  would  it  weigh  at  m, 
1,000  miles  below  its  surface  ?    6.  What  at  n,  o,  and 
c,  respectively  2,000,  3,000,  and  4,000  miles  below  the 
surface  ?  c.  What  at  6,  d,  e,  and  i,  respectively  4,000, 
8,000,  12,000,  and  2,000  miles  above  the  earth's  sur- 
face ? 

13.  a.  What  is  a  vertical  line  ?     6.  What  angle  does  it  make  with  the 
frame  of  a  spirit  level  when  in  position  ? 

14.  A  body  weighs  100  pounds  at  the  earth's  surface.     At  what  two 
places  would  its  weight  on  a  spring  balance  be  50  pounds  ? 

15.  If  the  acceleration  at  sea-level  be  32.2  feet,  what  is  it  5  miles  above 
sea-level  ? 


FIG.  90. 


124  MOLAR    DYNAMICS. 


CHAPTER   III. 

PROPERTIES   OF   MATTER. 

SECTION  I. 

CONSTITUTION    OF    MATTER. 

101.  Minuteness  of  particles  of  matter.  The  "molecule.  — 
Physiology  teaches  us  that,  in  order  to  smell  any  substance, 
we  must  take  into  our  nostrils,  as  we  breathe,  small  particles 
of  that  substance  which  are  floating  in  the  air.  The  air,  for 
several  meters  around,  is  sometimes  filled  with  fragrance  from 
a  rose.  You  cannot  see  anything  in  the  air,  but  it  is,  never- 
theless, filled  with  a  very  fine  dust  that  floats  away  from  the 
rose.  At  sea  the  odor  of  rosemary  renders  the  shores  of 
Spain  distinguishable  long  before  they  are  in  sight.  A  grain 
of  musk  will  scent  a  room  for  many  years,  by  constantly 
sending  forth  into  the  air  a  dust  of  musk.  Though  the 
number  of  particles  that  escape  must  be  countless,  yet  they 
are  so  small  that  the  original  grain  does  not  lose  perceptibly 
in  weight. 

These  instances,  and  numerous  others  of  common  obser- 
vation, give  us  only  a  feeble  conception  of  the  minuteness 
of  particles  of  matter  and  of  its  extreme  divisibility.  Yet 
the  smallest  particle  of  dust  of  rosemary  or  musk,  and  the 
smallest  particle  of  any  substance  which  can  be  obtained  by 
any  mechanical  means,  is  very  large  in  comparison  with 
bodies  called  molecules ,  which,  of  course,  are  too  small  to  be 
seen,  but  of  whose  existence  we  have  ample  evidence.  A 
single  simple  example  of  the  proofs  of  their  existence,  though 
by  no  means  the  most  conclusive,  must  suffice  at  this  place. 


EXPANDED 
STATE 


THEORY    OF    THE    CONSTITUTION    OF    MATTER.       125 

Matter,  e.y.  gold  or  water,  is  either  continuous  as  it  appears 
to  the  eye  or  it  is  discontinuous,  granular,  composed  of  distinct 

particles  (called  molecules)  somewhat  as  rep-  ,'. 

resented  in  Fig.  91.     Matter  is  compressible  .';':'.•'.'.•  .'-V- 

and    expansible.     On    the    supposition   that 

matter   is    continuous,  these    properties   are 

unexplaiiiable ;    but  on  the  supposition  that 

matter   is    molecular,    these    properties    are 

easily  explainable.     A  change  of  volume  by 

contraction    or    expansion   means    simply   a 

coming  together  or  a  separation  of  the  molecules  composing 

the  body,  as  represented  in  Fig.  91. 

102.  Theory  of  the  constitution  of  matter.  —  For   reasons 
which  will  appear  as  our  knowledge  of  matter  is  extended, 
physicists  have  generally  adopted  the  following  theory  of  the 
constitution  of  matter  :    Every  body  of  matter  except  the  mole- 
cule is  composed  of  exceedingly  small   disconnected  particles, 
called  molecules.     No  two  molecules  of  matter  in  the  universe 
are  in  permanent  contact  with  each  other.     Every  molecule  is  in 
quivering  motion,  moving  back  and  forth  between  its  neighbors, 
hitting  and  rebounding  from  them.      When  we  heat  a  body  we 
simply  cause  the  molecules  to  move  more  rapidly  through  their 
spaces;   so  they  strike   harder  bloivs  on  their   neighbors,   and 
usually  push  them  away  a  very  little  ;  hence  the  body  expands. 

103.  Porosity.  —  If  the  molecules  of  a  body  are  never  in 
contact  except  at  the  instants   of  collision,  it  follows  that 
there  are  spaces  between  them.    These  spaces  are  called  pores. 

All  matter  is  porous  ;  thus  water  may  be  forced  through  the 
pores  of  cast  iron ;  and  gold,  one  of  the  densest  of  substances, 
absorbs  liquid  mercury. 

Impenetrability1   may   be  affirmed  of  molecules,  but  not 

JThe  doctrine  of  impenetrability  declares  that  "Two  bodies  of  matter  cannot 
occupy  the  same  space  at  the  same  time."  In  its  strict  scientific  sense  this  doctrine 
is  as  axiomatic  as  the  statement  that  "  A  body  cannot  be  in  two  places  at  the  same 
time." 


126  MOLAR    DYNAMICS. 

necessarily  of  masses.  The  term  pore,  in  physics,  is  restricted 
to  the  invisible  spaces  that  separate  molecules.  The  cavities 
that  may  be  seen  in  a  sponge  are  not  pores,  but  holes  ;  they 
are  no  more  entitled  to  be  called  pores,  than  the  cells  of  a 
honeycomb  or  the  rooms  of  a  house  are  entitled  to  be  called, 
respectively,  the  pores  of  the  honeycomb  or  of  the  house. 

By  means  of  delicate  calculations,  physicists  ascertain  approxi- 
mately the  probable  size  of  the  molecule.  Lord  Kelvin  estimates 
that  the  diameter  of  the  molecules  of  a  gas  cannot  be  less  than  one 
five-hundred-millionth  of  a  centimeter.  The  minimum  particle 
visible  to  the  eye  is  a  cube  one  four-thousandth  of  a  millimeter  on  a 
side.  Such  a  cube  contains  from  sixty  to  one  hundred  million 
molecules. 

"The  kinetic  theory  of  gases  (p.  271)  teaches  that  in  a  cubic  inch 
of  any  gas  at  atmospheric  pressure  and  at  ordinary  temperatures 
there  are  about  3  X  10'20  detached  particles  absolutely  similar  and 
equal  to  one  another.  Here  we  reach  the  limit  of  our  present 
knowledge  as  to  division  of  matter."  (TAIT.) 

104.    Atomic  theory  of  matter.     Atoms. 

The  theory  given  above  assumes  that  the  molecule  is  the  limiting 
particle  of  possible  physical  division,  i.e.  the  smallest  particle  of  any 
substance  which  can  preserve  the  properties  of  that  substance  ; 
hence  the  molecule  is  sometimes  termed  the  "physicist's  unit." 
The  chemist  finds  it  necessary  to  assume  that  the  molecule  is  capable 
of  a  still  further  subdivision,  a  division  which  results  in  a  complete 
change  in  the  character  of  the  substance  operated  on.  Thus  a 
molecule  of  sugar  when  subjected  to  chemical  processes,  which  are 
virtually  chemical  divisions,  yields  carbon,  hydrogen,  and  oxygen, 
substances  entirely  unlike  sugar.  These  still  smaller  particles 
obtained  by  the  division  of  the  molecule  are  called  atoms.  The 
atomic  theory  assumes  that  the  atom,  as  the  word  etymologically 
signifies,  is  indivisible,  and  it  may  be  termed  the  "  chemist's  unit." 
An  atom  is  indestructible  and  unchangeable.  About  seventy  differ- 
ent kinds  of  atoms  have  been  discovered.  These  constitute  the 
so-called  elementary  substances.  All  other  substances  are  compounds 
of  certain  of  these  elements  of  varying  degrees  of  complexity.  A 
molecule  consists  of  a  group  of  atoms  bound  together  by  chemical 


THE   PECULIAR   PROPERTIES    OF   MATTER.  127 

forces  usually  termed  chemical  affinity,  and  a  mass  consists  of  a 
group  of  molecules  which  may  or  may  not  be  bound  together  by  a 
physical  or  molecular  force  called  cohesion. 


SECTION  II. 

THE    STATES    OF    MATTER    AND    THEIR    PECULIAR    PROPERTIES. 

105.  Solids,  liquids,  and  gases.  —  In  popular  language  there 
are  said  to  be  three  states  of  matter,  the  solid,  the  liquid,  and 
the  gaseous. 

Solids  preserve  a  definite  volume  and  shape  when  left  to 
themselves  ;  liquids  tend  to  preserve  a  definite  volume  only, 
while  their  shape  conforms  to  that  of  the  containing  vessel ; 
gases  tend  to  preserve  neither  a  definite  volume  nor  shape,  but 
conform  not  only  in  shape  but  in  volume  to  the  containing 
vessel,  no  matter  how  large  this  may  be.  We  may  have  a 
vessel  half  full  of  liquid,  but  a  mass  of  gas  always  occupies 
the  whole  of  a  containing  vessel,  however  small  the  quantity 
of  gas.  Gases  tend  to  expand  indefinitely  and  to  assume  an 
infinite  volume  with  a  correspondingly  small  density.  Solids 
and  liquids  may  have  free  surfaces,  gases  cannot  retain  per- 
manently a  free  bounding  surface  independent  of  the  contain- 
ing vessel. 

Which  of  the  three  states  any  portion  of  matter  assumes  depends 
upon  its  temperature  and  pressure.  Just  as  at  ordinary  pressures  of 
the  atmosphere  water  is  a  solid  (i.e.  ice),  a  liquid,  or  a  gas  (i.e.  steam), 
according  to  its  temperature,  so  any  substance  may  be  made  to 
assume  any  one  of  these  forms  unless  a  change  of  temperature 
causes  a  chemical  change,  i.e.  causes  it  to  break  up  into  other  sub- 
stances. For  example,  wood  cannot  be  melted,  because  it  breaks 
up  into  charcoal,  steam,  etc.,  before  the  melting-point  is  reached. 
In  order  that  matter  may  exist  in  a  liquid  (and  sometimes  in  a  solid) 
state,  a  certain  definite  pressure  is  required.  Ice  vaporizes,  but 
does  not  melt  (i.e.  liquefy)  in  a  space  from  which  the  air  (and  con- 
sequently atmospheric  pressure)  has  been  removed.  Solid  carbonic 


128  MOLAIl    DYNAMICS. 

acid  vaporizes,  but  does  not  melt  unless  the  pressure  is  greater 
than  the  ordinary  atmospheric  pressure.  Charcoal  has  been  vapor- 
ized, but  has  never  been  liquefied,  undoubtedly  because  sufficient 
pressure  has  never  been  used. 

As  regards  the  temperature  and  pressure  at  which  different  sub- 
stances assume  the  different  states,  there  is  great  diversity.  Oxygen 
and  nitrogen  gases  liquefy  and  solidify  only  at  extremely  low  tem- 
peratures ;  and  then,  only  under  great  pressure.  On  the  other 
hand,  certain  substances,  as  quartz  and  lime,  are  liquefied  only 
by  the  most  intense  heat. 

106.  Fluids.  —  The  term  implies  the  property  of  /lowing. 
Since   both  liquids   and   gases   possess   this    property  in  an 
eminent  degree  in  consequence  of  great  freedom  of  motion  of 
their  molecules  around  one  another,  they  are  both  included 
under  the  common  term  fluid.    Further  on  it  will  be  seen  that 
one  of  the  chief  distinctions  between  a  solid  and  a  fluid  is 
that  the  former  possesses  rigidity,  while  the  latter  does  not. 

107.  Vaporous  state  ;  critical  state. 

Closer  study  makes  evident  that  the  above  classification  is  purely 
arbitrary.  The  three  states  of  matter  sometimes  merge  into  one 
another  so  that  there  remains  no  distinct  line  of  demarkation 
between  them.  For  example  there  is  a  state  which  may  be  regarded 
as  intermediate  between  the  liquid  and  the  gaseous,  called  the 
vaporous  state.  If  a  substance  in  the  gaseous  form  be  compressed 
or  cooled  to  such  an  extent  that  it  will  suffer  but  little  further 
compression  or  cooling  without  passing  into  the  liquid  state,  it 
possesses  in  this  state  certain  peculiar  properties  and  is  known  by 
the  name  of  vapor.  A  vapor  may  be  defined  as  a  gas  near  its  con- 
densing point.  When  matter  is  at  a  temperature  and  under  a  pres- 
sure such  that  if  heated  a  little  more  it  becomes  a  vapor,  or  if 
allowed  to  cool  a  little  more  it  becomes  a  liquid,  it  is  said  to  be  in 
the  critical  state.  In  this  semi-liquid  state  the  gaseous  and  liquid 
states  meet  and  are  indistinguishable.  The  highest  temperature 
at  which  this  occurs  is  called  the  critical  temperature,  and  the 
highest  pressure  the  critical  pressure.  A  vapor  may  be  defined,  also, 
as  any  gaseous  substance  at  a  temperature  below  its  critical  temper- 
ature. 


MOLECULAR    FORCES.  129 

For  example,  carbon  dioxide  at  31°  and  under  a  pressure  of  73 
atmospheres  is  in  a  critical  state.  Heated  a  little  it  certainly  becomes 
gaseous ;  cooled  a  little  it  as  certainly  assumes  the  properties  of  a 
liquid,  since  it  is  far  less  compressible.  But  if  the  pressure  be 
maintained,  the  transition  from  one  to  the  other  is  not  recognizable. 

108.    Ultragaseous  or  fourth  state  of  matter. 

Air  has  been  rarefied  to  the  three-hundred-millionth  of  its  normal 
density.  But  when  gaseous  matter  is  rarefied  to  even  a  millionth 
of  the  density  of  air  at  sea-level,  it  exhibits  extraordinary  properties 
quite  as  different  from  the  gaseous  as  this  is  from  the  liquid  state, 
so  that  some  are  disposed  to  consider  that  there  is  an  ultragaseous 
or  fourth  state  of  matter. 


SECTIOX  III. 

MOLECULAR    FORCES. 

109.  Molecular  attractive  forces. — Many  of  the  properties 
of  matter  are  due  to  molecular  forces,  some  of  which  now 
demand  our  attention.  For  convenience  we  call  bodies  of 
appreciable  size  molar  (massive)  bodies,  or  masses,  in  dis- 
tinction from  molecules  (bodies  of  very  small  mass).  Action 
between  molar  bodies,  usually  at  sensible  distances,  is  called 
molar  force ;  action  between  molecules,  always  at  insensible 
distances,  is  called  molecular  force.  According  to  the  theory 
of  the  constitution  of  matter  the  molecules  of  every  mass  are 
in  ceaseless  motion,  hitting  and  rebounding  from  one  another. 
This  tends  to  drive  the  molecules  apart.  In  gaseous  masses 
the  molecules  move  without  restraint  j  hence  gaseous  bodies 
always  tend  to  expand. 

In  solids  and  liquids  the  molecules  are  held  under  the 
action  of  a  very  powerful  attractive  force,  called  cohesion, 
which  prevents  their  separation  except  under  the  action  of 
considerable  external  force.  It  is  the  force  which  resists  an 
effort  tending  to  break,  tear,  or  crush  a  body.  The  tenacity  or 


130  MOLAR    DYNAMICS. 

tensile  strength  of  solids  and  liquids,  i.e.  the  resistance  which 
they  offer  to  being  pulled  apart,  is  due  to  this  force.  It  is 
usually  greater  in  solids  than  in  liquids,  and  is  entirely 
wanting  in  a  true  gas. 

110.  Strain,  rigidity,  elasticity.  —  Strain  means  change  of 
size,  change  of  shape,  or  deformation  of  any  kind.  Change- 
of-size  strain  is  called  compression  or  dilatation,  and  the 
resistance  of  matter  to  it  is  called  elasticity  of  volume. 
Change-of-shape  strain,  such  as  in  flexion,  torsion,  etc.,  is 
called  distortion,  and  the  resistance  to  it  manifests  itself 
either  as  elasticity  of  figure,  or  rigidity. 

Elasticity  is  that  property  in  virtue  of  which  a  solid  tends  to 
recover  its  size  and  shape,  and  a  fluid  its  size,  after  defor- 
mation. Solids  are  remarkable  for  high  rigidity.  A  per- 
fectly rigid  solid  is  one  which,  when  a  force  is  applied  to  it 
in  any  way,  suffers  no  strain  before  breaking.  No  body  is 
absolutely  rigid,  though  some  bodies  are  approximately  so. 
If  the  stress  between  the  molecules  in  opposition  to  the 
distorting  force  continue  constant,  regardless  of  the  time  the 
strain  is  kept  up,  and  restore  the  body  to  its  normal  con- 
dition immediately  on  the  removal  of  the  distorting  force, 
without  any  permanent  strain  or  "  set,"  the  body  is  said  to 
be  perfectly  elastic.  All  fluids  are  perfectly  elastic,  and  a 
few  solids  are  approximately  so,  such  as  ivory,  steel,  and 
glass. 

*[f  a  solid  have  little  or  no  tendency  to  recover  its  size  and 
shape  after  distortion,  it  is  said  to  be  plastic  or  inelastic. 
Such  substances  are  putty,  wet  clay,  and  dough.  A  great 
number  of  substances  are  elastic  when  the  distorting  forces 
are  small,  but  break  or  receive  a  "  set "  when  these  forces 
are  too  great.  They  are  said  to  be  elastic  "  within  certain 
limits,"  called  the  limits  of  elasticity.  If  strained  beyond 
those  limits,  they  become  more  or  less  plastic.  Hence  the 
springs  of  a  buggy  sometimes  become  set  from  bearing  a  too 


VISCOSITY.  131 

heavy  load  and  lose  permanently  much,  of  their  elasticity ; 
i.e.  they  become  in  a  degree  plastic. 
111.     Viscosity. 

Experiment  1.  —  Support  in  a  horizontal  position,  by  one  of  its  extrem- 
ities, a  stick  of  sealing-wax,  and  suspend  from  its  free  extremity  an 
ounce  weight,  and  let  it  remain  in  this  condition  several  days,  or  perhaps 
weeks.  At  the  end  of  the  time  the  stick  will  be  found  permanently  bent. 
Had  an  attempt  been  made  to  bend  the  stick  quickly,  it  would  have  been 
found  quite  brittle. 

It  may  seem  like  an  abuse  of  the  term  to  call  sealing-wax 
a  fluid,  yet  the  experiment  shows  it  to  be  a  fluid,  or  at  least 
to  possess  fluidity,  or  freedom  of  motion  of  its  molecules 
around  one  another,  in  a  small  degree.  Resistance  to  deforma- 
tion due  to  the  friction  of  the  molecules  of  a  body  in  sliding 
over  one  another  is  called  viscosity.  Bodies  that  slowly  suffer 
continuous  and  permanent  deformation  under  the  action  of  a 
continuous  stress  are  said  to  be  viscous.  A  lump  of  pitch  in 
course  of  time  loses  its  sharpness  of  outline  and  flows  down 
hill  of  its  own  weight.  It  is  very  viscous.  Cold  molasses  is 
quite  viscous,  but  as  its  temperature  is  raised  its  viscosity 
diminishes  and  it  becomes  more  and  more  plastic  or  mobile. 
A  perfectly  rigid  solid  is  one  of  infinite  viscosity.  A  perfect 
fluid  is  a  fluid  which  possesses  no  viscosity.  Gases  are 
viscous  to  some  extent  and  are  therefore  imperfect  fluids. 

Bodies  surrounded  by  air  have  on  their  surfaces  an  adherent  film 
of  air.  When  they  move,  this  film  rubs  against  the  surrounding  air, 
and  thus  their  movements  are  retarded  by  friction  in  the  air.  To 
the  viscosity  of  the  air  is  due  in  part  the  retardation  of  the  velocity 
of  falling  bodies.  A  penny  and  a  piece  of  tissue  paper  fall  with 
equal  accelerations  in  a  vacuum  (p.  120),  but  in  the  air  the  penny 
falls  more  rapidly  because  it  presents  less  surface  and  therefore  is 
retarded  less  in  proportion  to  its  weight  by  the  friction  of  the  air. 

Falling  water  is  retarded  by  the  air ;  conversely,  air  is  dragged 
down  by  falling  water,  as  shown  by  the  following  experiment. 


132 


MOLAR    DYNAMICS. 


Experiment  2.  —  Take  a  long  glass  tube  A  (Fig.  92),  funnel-shaped 
at  one  end,  and  having  a  little  below  this  end 
a  short  branch  tube  a.  Pour  water  into  the 
funnel  and  observe  that  it  falls  in  a  con- 
tinuous stream  until  it  reaches  a,  but  below  ' 
this  point  it  is  broken  up  by  descending 
bubbles  of  air  which  it  drags  along  with  it 
after  coming  in  contact  with  the  air  at  a. 
If  direct  sunlight  be  allowed  to  strike  the 
tube,  the  interior  reflection  from  the  water 
in  this  part  of  the  tube  is  dazzling  and 
beautiful. 

Connect  with  a  by  means  of  a  rubber 
tube  another  short  piece  of  glass  tube  6,  and 
introduce  the  latter  into  a  tumbler  of  water. 
The  water  descending  in  A  exhausts  the  air 
in  b  and  the  outside  atmospheric  pressure 
causes  the  water  in  the  tumbler  to  ascend 
this  tube  6,  and  thus  the  tumbler  may  be 
emptied.  If  a  closed  vessel  B  be  connected  with  a,  a  high  vacuum 
may  be  obtained  in  it. 

Experiment  3.  —  Pour  water  from  an  elevation  upon  a  still  body  of 
water  below  and  observe  the  bubbles  of  air  which  form  in  the  water,  the 
air  being  dragged  by  the  falling  current  to  a  considerable  depth  in  the 
liquid. 

112.  Hardness.  —  Hardness  is  resistance  to  abrasion  or 
scratching. 

To  enable  us  to  express  degrees  of  hardness,  the  following 
table  of  reference  is  generally  adopted  :  — 


FIG.  92. 


MOHR'S  SCALE  OF  HARDNESS. 


1.  Talc. 

2.  Gypsum  (or  Rock-Salt). 

3.  Calcite. 

4.  Fluor-Spar. 

5.  Apatite. 


6.  Orthoclase  (Feldspar). 

7.  Quartz. 

8.  Topaz. 

9.  Corundum. 
10.  Diamond. 


CAPILLARITY.  183 

By  comparing  a  given  substance  with  the  substances  in  the 
table,  its  degree  of  hardness  can  be  indicated  approximately. 
Thus  "H  =  7"  means  that  the  body  is  about  as  hard  as  quartz. 

113.  Malleability,  ductility.  —  Solids  which  possess  that 
kind  of  fluidity  which  renders  them  susceptible  of  being  rolled 
or  hammered  out  into  sheets  are  said  to  be  malleable.  Most 
metals  are  highly  malleable.  Gold  may  be  hammered  so  thin 
as  to  be  transparent,  or  to  a  thickness  of  one  three-hundred- 
thousandth  of  an  inch.  Most  substances  that  are  malleable 
are  susceptible  also  of  being  drawn  out  into  fine  threads, 
e.g.  wire  of  different  metals.  Such  substances  are  said  to  be 
ductile.  Platinum  has  been  drawn  into  wire  .000165  inch 
thick,  or  so  fine  as  to  be  scarcely  visible  to  the  unaided  eye. 


SECTION  IV. 

CAPILLARITY. 

114.  Cohesion  of  liquids.  —  Clean  glass  is  wet  by  water. 
If  a  glass  plate  be  dipped  into  water  and  then  withdrawn,  a 
layer  of  water  clings  to  the  glass.  When  the  glass  is  with- 
drawn, water  is  torn  from  water,  and  not  glass  from  water. 
This  shows  that  the  attraction  of  the  molecules  of  water  for 
one  another  is  weaker  than  the  attraction  between  glass  and 
water.  Or  if,  to  save  words,  we  call  the  attraction  between 
the  solid  and  the  liquid  adhesion,  then  we  may  say  that  the 
cohesion  between  the  molecules  of  the  water  is  weaker  than 
the  adhesion  between  the  glass  and  the  water. 

Clean  glass  is  not  wet  by  clean  mercury,  which  shows  that 
the  adhesion  between  glass  and  mercury  is  not  as  great  (about 
one  third  as  great)  as  the  cohesion  in  mercury.  Generally 
speaking  a  solid  is  wet  by  a  liquid  when  the  adhesion  of  the 
solid  to  the  liquid  is  greater  than  the  cohesion  of  the  liquid, 
and  is  not  wet  when  the  cohesion  is  greater  than  the  adhesion. 


134  MOLAR   DYNAMICS. 

115.  Surface,  tension,  —  When  a  rubber  band  is  strained  or 
stretched,  it  is  said  to  be  in  a  state  of  tension,  and  there  exists 
between  its  molecules  a  contractile  or  resilient  stress. 

In  liquids  the  molecules  are  within  the  limits  of  one  another's 
attractions,  which  accounts  for  a  greater  or  less  viscosity  or 
hindrance  of  flow  and  also  for  a  certain  phenomenon  called 
surface  tension.  Every  liquid  behaves  as  if  a  thin  film  forming 
its  external  layer  were  in  a  state  of  tension,  or  were  exerting 
a  constant  effort  to  contract. 

It  is  not  within  the  scope  of  this  book1  to  explain  in  full 
the  dynamics  of  the  molecular  forces  by  which  this  result  is 
brought  about ;  it  must  suffice  to  call  the  attention  of  the 
student  to  the  peculiar  condition,  with  reference  to  mutual 
attractions,  of  those  molecules  which  compose  the  surface  film. 
In  the  interior  of  a  liquid  each  molecule  is  surrounded  by 
other  similar  molecules  and  the  position  which  it  assumes  is 
that  in  which  it  is  acted  upon  equally  in  all  directions,  and 
there  is  nothing  to  render  the  mutual  attractions  manifest. 
At  a  free  surface,  however,  the  molecules  can  be  acted  upon 
only  by  others  lying  internal  to  them.  The  result  is  a  system 
of  forces  acting  at  right  angles  to  the  free  surface  of  the 
liquid,  and  tending  to  reduce  the  free  surface  to  the  least 
possible  area.  This  tendency  of  a  liquid  surface  to  contraction 
means  that  it  acts  like  an  elastic  membrane,  equally  stretched 
in  all  directions,  and  by  a  constant  tension.  In  the  case  of 
pure  water  at  20°  C.  this  tension  is  about  81  dynes  per  linear 
centimeter. 

Experiment.  —  Form  a  soap-bubble  at  the  orifice  of  the  bowl  of  a 
tobacco  pipe,  and  then,  removing  the  mouth  from  the  pipe,  observe  that 
the  tension  of  the  two  surfaces  (exterior  and  interior)  of  the  bubble  drives 
out  the  air  from  the  interior  and  finally  the  bubble  contracts  to  a  flat 
sheet  of  minimum  area. 

1  The  student  who  is  desirous  of  knowing  more  of  this  interesting  subject  may 
consult  the  article  "  Capillarity,"  by  Maxwell,  in  the  Encyclopaedia  Britannica. 


CAPILLARY    PHENOMENA.  135 

• 

As  a  consequence  of  surface  tension,  every  body  of  liquid  tends  to 
assume  the  spherical  /or?n,  since  the  sphere  has  less  surface  than  any 
other  form  having  equal  volume.  In  large  bodies  the  distorting  forces 
due  to  gravity  are  generally  sufficient  to  disguise  the  effect ;  but  in  small 
bodies,  as  in  drops  of  water  or  mercury,  it  is  apparent.  Again,  if  the 
distorting  effect  of  weight  be  eliminated  in  any  way,  as  by  immersing  a 
quantity  of  oil  in  a  mixture  of  water  and  alcohol  of  its  own  density,  or  by 
replacing  the  central  portion  of  the  body  by  a  fluid  much  lighter  than  its 
own  kind,  as  in  the  case  of  a  soap-bubble,  the  sphere  is  the  resulting  form. 

116.  Capillary  phenomena.  —  Surface  tension  is  Toy  no  means 
peculiar  to  liquids.  The  surfaces  of  all  bodies  tend  to  con- 
tract. But  since  gases  have  no  surfaces  of  their  own,  and  the 
rigidity  of  solids  prevents  an  alteration  of  shape,  it  is  obvious 
why  liquids  show  the  effects  of  surface  tension  most  readily. 
But  the  surface  tensions  of  solids  and  gases  perform  their 
part  in  determining  certain  phenomena.  For  example,  if  a 
glass  rod  be  thrust  vertically  into  water  so  as  to  leave  a  part 
projecting  into  the  air,  the  surface  of  the  water  does  not  meet 
the  rod  at  right-angles,  but  is  turned  up  so  as  to  form  a  very 
small  angle1  with  the  surface  of  the  glass,  as  acb  (Fig.  93). 
Here  the  three  substances,  water,  glass,  and  air,  are  brought 
in  contact  and  there  are  a  triplet  of  tensions  in  operation  the 
resultant  of  which  is  a  force  which  pulls  the  water  up  against 
the  glass  wall.  On  the  other  hand  if  mercury,  glass,  and  air 
be  brought  in  contact,  the  relation  between  the  triplet'  of 
forces  becomes  so  changed  as  to  cause  the  mercury  to  meet  the 
glass  at  a  very  large  angle,  about  135°.  It  thus  seems  that 
when  a  solid,  a  liquid,  and  a  gas  are  in  contact,  their  boundary 
surfaces  form  contact  angles  with  one  another  determined  by 
their  relative  surface  tensions. 

If  a  glass  tube  x  (Fig.  94)  of  capillary  (hair-like)  bore  be 
thrust  into  water,  the  water  will  rise  in  the  bore  considerably 
above  the  general  level  outside.  If  a  similar  tube  y  (Fig.  95) 

1  If  the  glass  be  quite  clean  the  angle  is  0.  If  not  clean,  it  may  reach,  and  even 
exceed,  90°. 


136 


MOLAR    DYNAMICS. 


be  thrust  into  mercury,  the  mercury  within  the  bore  will  be 
depressed  below  the  surface  outside.  Phenomena  of  this  kind 
are  called  capillary  phenomena.  The  surfaces  of  the  liquids 
inside  the  bores  are  curved,  the  surface  of  water  being  concave 
and  that  of  mercury  convex.  The  size  of  the  bore  of  the 


Mercury 
FIG.  95. 


FIG.  96. 


tubes  x  and  y  is  greatly  exaggerated  in  order  to  show  this 
more  plainly.  The  concavity  and  convexity  of  these  interior 
surfaces  are  a  necessary  consequence  of  the  angles  of  contact 
with  which  these  liquids  meet  glass.  It  remains  only  to 
explain  the  elevation  and  depression  of  the  column  of  liquid 
in  the  tube.  This  may  be  done  in  part  by  analogy.  Let  AB 
(Fig.  96)  represent  a  clothes  line  suspended  slackly  between 
two  posts.  From  this  line  hang  by  strings  small  stones 
a,  b,  Cj  etc.  If  the  hempen  line  become  wet,  as  in  a  rain,  it 


CAPILLARY    PHENOMENA. 


137 


contracts  and  straightens,  as  shown  by  the  dotted  line  AB. 
In  other  words,  the  contractile  force  which  is  exerted  obliquely 
(e.g.  nm  Fig.  96)  is  resolvable  into  two  forces,  one  of  which 
is  horizontal  and  the  other  is  vertically  upward  ;  the  latter 
tends  to  elevate  the  stones.  In  a  similar  manner  the  curved 
surfaces  of  water  and  mercury  tend  to  contract  and  become 
flat.  In  the  case  of  the  water  surface  (which  is  concave)  the 
contractile  force  tends  to  elevate  the  pendent  liquid ;  but  in 
the  case  of  the  mercury  surface  (which  is  convex)  the  tendency 
is  to  produce  depression.  On  the  nature  of  the  curvature 
depends  the  direction  in  which  the  contractile  force  acts  on 
the  pendent  liquid.  Now  it  is  evident  that  water  will  be 
drawn  up  by  this  contractile  force  until  the  weight  of  the 
column  balances  this  force ;  and  mercury  will  be  depressed 
until  the  force  is  balanced  by  the  pressure  of  the  mercury  out- 
side the  tube.  Capillary  phenomena  are,  therefore,  phenomena 
of  surface  tension. 

The  phenomena  of  capillary  action  are  well  shown  by  placing 
various  liquids  in  U-shaped  glass  tubes  having  one  arm 
reduced  to  a  capillary  size,  as  A 
and  B  in  Fig.  97.  Mercury  poured 
into  A  assumes  convex  surfaces 
in  both  arms,  but  does  not  rise  as 
high  in  the  small  arm  as  it  stands 
in  the  large  arm.  Pour  water  into 
B,  and  all  the  phenomena  are  re- 
versed. Fig.  98  shows  the  forms 
that  the  surfaces  of  water  and 
mercury  take  when  contained  in  the  same  glass  tube. 

The  following  laws  of  capillary  action  may  be  verified  by 
experiment :  — 

I.  Liquids  rise  in  tubes  when  they  wet  them,  and  are  depressed 
when  they  do  not. 


FIG.  97. 


138  MOLAR   DYNAMICS. 

II.   The  elevation  or  depression  varies  inversely  as  the  diameter 
of  the  bore. 

III.  The  elevation  and  depression  vary  with  the  nature  of  the 

liquids  employed,  and  with  the  substance  of  the  tube. 

IV.  The  elevation  or  depression  varies  inversely  with  the  tem- 

perature. 

SECTION  V. 

DIFFUSION    OF    FLUIDS. 

117.  Other  molecular  phenomena. 

Besides  the  phenomena  we  have  just  studied,  there  are  a  great 
many  others  depending  in  part  on  molecular  attraction,  but  much 
more  on  molecular  motions,  of  which  we  learned  on  p.  125  and 
which  we  now  must  consider  more  in  detail. 

The  molecules  of  all  bodies  are  constantly  in  a  state  of  motion. 
The  higher  the  temperature  the  greater  are  their  velocities.  In  a 
solid  "a  molecule,  though  in  continual  motion,  never  gets  beyond 
a  certain  very  small  distance  from  its  original  position  in  the  body. 
In  fluids  there  is  no  restriction  to  the  excursions  of  a  molecule. 
True  the  molecule  travels  only  a  very  small  distance  before  it 
encounters  another  molecule ;  but  after  this  encounter  there  is 
nothing  which  determines  the  molecule  rather  to  return  towards  the 
place  whence  it  came  than  to  push  its  way  into  new  regions.  Hence 
in  fluids  the  path  of  a  molecule  is  not  confined  to  a  limited  region, 
but  may  penetrate  to  any  part  of  the  space  occupied  by  the  fluid." 
MAXWELL. 

118.  Diffusion  of  liquids. 

Experiment  1.  —  Partially  fill  a  glass  jar  (Fig.  99)  with  water. 
Then  introduce  beneath  the  water,  by  means  of  a  long  tunnel,  a 
concentrated  solution  of  sulphate  of  copper.  The  lighter  liquid 
rests  upon  the  heavier,  and  the  line  of  separation  between  the  two 
liquids  is  at  first  distinctly  marked.  But  in  the  course  of  days  or 
weeks  this  line  will  gradually  become  obliterated,  the  heavier  blue 
liquid  will  gradually  rise,  and  the  lighter  colorless  liquid  will 
descend,  till  they  become  thoroughly  mixed. 

Experiment  2.  —  Take  about  1  cc  of  bisulphide  of  carbon,  color 
it  by  dropping  into  it  a  small  particle  of  iodine,  and  pour  this 


DIFFUSION    OF    GASES. 


139 


FIG.  99. 


colored  solution   into   a  test-tube   nearly   filled  with  water.     The 

colored  liquid,  being  heavier  than  the  water,  sinks 

directly  to  the   bottom,  and  shows  no  tendency  to 

mix  with  the  water.     But  in  the  course  of  time  you 

discover  that  the  colored  liquid  diminishes  in  quantity, 

and  finally  disappears.       The  peculiar  odor  of  this 

substance  which  pervades  the  air  in  the  vicinity  shows 

that  a  considerable  portion  has  evaporated.     But  it 

must  have  worked  its  way  gradually  through  the 

water  above  it. 

If,  in  the  last  two  experiments,  you  examine  the 
liquid  with  a  microscope  during  the  operation,  you 
will  not  be  able  to  trace  any  currents ;  hence  the  motion  of  the  liquids 
is  not  in  mass,  but  by  molecules  —  a  true  intermolecular  motion. 

An  intermingling  of  the  molecules  of  two  liquids  caused  by  their 
own  motions  is  called  diffusion  of  liquids. 

119.    Diffusion  of  gases. 

Experiment  3.  —  Fill  a  test-tube  with  oxygen  gas,  and  thrust  into 
it  a  lighted  splinter  ;  the  splinter  burns  much  more  rapidly  than  in 
the  air.  Fill  another  tube  with  hydrogen  gas,  and  keep 
the  tube  inverted  (for,  this  gas  being  about  14.4  times 
as  light  as  air,  there  will  be  no  danger  of  its  falling  out). 
Thrust  in  a  lighted  splinter ;  the  gas  takes  fire,  and  burns 
with  a  pale  flame  at  the  mouth  of  the  tube.  Next  fill 
one  tube  with  oxygen  and  the  other  with  hydrogen 
gas,  and  place  the  mouth  of  the  latter  over  the  mouth 
of  the  former,  as  in  Fig.  100.  In  about  a  minute  apply 
a  lighted  splinter  to  the  mouth  of  the  tube  (let  the  mouth 
of  each  tube  be  freely  open  to  prevent  accident) ;  a  slight 
explosion  takes  place  in  each  instance.  It  is  apparent 
that  although  the  oxygen  gas  is  14.4  times  as  heavy  as 
the  hydrogen,  some  of  it  has  risen  into  the  upper  tube, 
while  some  of  the  lighter  hydrogen  has  descended  into 
the  lower  tube,  and  the  two  gases  have  become  diffused. 

There  are  liquids  between  which  diffusion  does  not 
take  place.  But  it  does  take  place  between  any  two 
gases  whenever  they  are  placed  in  contact. 

In  consequence  of  this  universal  tendency  to  diffusion, 
gases  will  not  remain  separated  —  i.e.  a  lighter  resting 
FIG.  100.  upon  a  heavier,  as  oil  rests  upon  water.  This  is  of 


140 


MOLAR    DYNAMICS. 


immense  importance  in  the  economy  of  nature.  The  largest  portion 
of  our  atmosphere  consists  of  a  mixture  of  oxygen  and  nitrogen 
gases.  There  are  always  present  also  small  quantities  of  other  gases, 
such  as  carbon  dioxide,  ammonia  gas,  and  various  other  gases, 
which  are  generated  by  the  decomposition  of  organic  matter.  These 
gases,  obedient  to  gravity  alone,  would  arrange  themselves  according 
to  their  weight,  —  carbonic-acid  gas  at  the  bottom,  or  next  the  earth, 
followed  respectively  by  oxygen,  nitrogen,  ammonia,  and  other  gases. 
Neither  animal  nor  vegetable  life  could  exist  in  this  state  of  things. 
But,  in  consequence  of  the  diffusibility  of  these  gases,  they  are 
found  intimately  mixed  and  in  the  same  relative  proportions, 
whether  in  the  valley  or  on  the  highest  mountain  peak. 

120.  Osmose,  or  diffusion  of  liquids  through  membranous  septa. 

Certain  liquids  when  separated  from  each  other  by  membranous 
septa  diffuse  through  these  septa,  and  the  diffusion  may  be  more 
rapid  than  when  no  septa  intervene.  Such  membranes  as  a  bladder, 
cow's  pericardium,  and  parchment  paper  are  especially  suited  to 
this  purpose.  Diffusion  through  septa  is  called  osmose.  There  is 
a  wide  range  of  relative  diffusibilities.  At  one  end  of  the  scale  are 
such  substances  as  solutions  of  urea,  common  salt,  and  such  sub- 
stances as  crystallize,  hence  called  crystalloids.  These  diffuse 
rapidly.  At  the  other  extreme  are  such  substances  as 
starch,  gum,  albumen,  gelatine,  and  glue-like  matter, 
called  colloids.  These  diffuse  very  slowly.  If  a  mixture 
composed  of  a  crystalloid  and  a  colloid  be  placed  in  a 
bladder,  for  instance,  and  the  bladder  be  suspended  in 
water,  the  crystalloid  will  rapidly  diffuse  through  the 
septum  while  the  colloid  will  diffuse  very  slowly.  In 
this  way  a  separation  of  the  two  substances  may  be 
effected.  Separation  by  this  process  is  called  dyalysis. 

121.    Osmose  of  gases. 

Experiment  4.  —  Seal  the  open  end  of  a  thin,  unglazed 
earthen  cup,  such  as  is  used  in  a  Bunsen   battery  (p. 
471),  with  plaster  of  Paris,  through  which  extends  a 
glass  tube.     Place  the  exposed  end  of  the  tube  in  a 
FIG.  101.     cup  of  colored  water.      Lower  a  glass  jar  rilled  with 
hydrogen  or  coal-gas  over  the  porous  cup,  as  in  Fig.  101.    Instantly 
air  is  forced  down  through  the  tube,  and  escapes  in  bubbles  from 


OSMOSE   OF    GASES. 


141 


the  colored  liquid.  The  gas  in  the  larger  vessel  forces  its  way 
through  the  pores  of  the  cup,  diffuses  through  the  air  contained  in 
it,  and  causes  an  unusual  pressure  on  the  colored  liquid,  as  is 
evinced  by  the  air  that  is  forced  out  through  it.  In  a  minute  remove 
the  glass  jar.  The  hydrogen  now  escapes  through  the  sides  of  the 
cup,  and  mixes  with  the  air  on  the  outside ;  a  partial  vacuum  is 
formed  in  the  cup,  and  water  rises  in  the  tube.  In  each  case  air 
passes  through  the  sides  of  the  porous  cup,  but  the  influx  and  efflux 
of  the  hydrogen  is  much  more  rapid  than  that  of  the  air. 

An   interesting  modification  of   this  apparatus  is  the  diffusion 
fountain  (Fig.  102).     By  passing  the  glass  tube  of  the  porous  cup 
through  the  cork  of  a  tightly -stoppered  vessel, 
and    having  another  glass   tube   pass  through 
another  perforation  in  the  same  cork,  water  is 
forced  out  in  a  jet  several  feet  in  hight,  when 
the  hydrogen  jar  is  held  over  the  porous  cup. 

Children  well  understand  that  toy  balloons, 
which  are  made  of  collodion  and  tilled  with 
coal-gas,  collapse  in  a  few  hours  after  they  are 
inflated.  This  is  caused  by  the  escape  of  the  gas 
by  osmose.  Nature  furnishes  an  illustration  of 
osmose  of  gases  in  respiration.  In  the  lungs 
the  blood  is  separated  from  the  air  by  the  thin, 
membranous  walls  of  the  veins.  Carbon  dioxide 
escapes  from  the  blood  through  these  septa,  and  oxygen  gas  enters 
the  blood  through  the  same  septa. 

The  phenomena  of  diffusion  both  in  liquids  and  gases  furnish  strong 
and  tangible  evidence  that  these  bodies  consist  of  molecules  in  a  state 
of  continual  motion. 


FIG.  102. 


142 


MOLAR    DYNAMICS, 


CHAPTER   IV. 

DYNAMICS   OF   FLUIDS. 

SECTION  I. 

TRANSMISSION    OF    PRESSURE. 

122.  Law  of  hydrostatic  and  pneumatic  transmission  of 
pressure.  —  That  branch  of  science  which  treats  of  liquids  in  a 
state  of  equilibrium  or  rest  is  called  hydrostatics ;  that  branch 
which  treats  of  liquids  in  motion  is  called  hydrokinetics ; 
and  that  branch  which  treats  of  the  dynamics  of  air  and  other 
gases  is  called  pneumatics.  With  the 
exception  of  phenomena  occasioned 
by  difference  in  compressibility  and 
expansibility,  liquids  and  gases  are 
subject  to  the  same  laws  and  may 
be  treated  together,  in  so  far  as  they 
are  alike,  under  the  common  term 
fluid. 

Experiment  1.  —  Fill  the  glass  globe  and 
cylinder  (Fig.  103)  with  water,  and  thrust 
the  piston  into  the  cylinder.  Jets  of  water 
will  be  thrown  not  only  from  that  aperture 
a  in  the  globe  toward  which  the  piston 
moves  and  the  pressure  is  exerted,  but  from 
all  the  apertures. 

If  a  finger  be  placed  loosely  over 
the  end  of  a  water  faucet,  spray  will 
be  thrown  to  equal  distances  in  all 
directions.  It  thus  appears  not  only 
that  external  pressure  is  exerted 
upon  that  portion  of  the  liquid  that  lies  in  the  path  of  the 


FIG.  IDS. 


TRANSMISSION   OF   PRESSURE.  143 

force,  but  that  it  is  transmitted  equally  to  all  parts  and  in  all 
directions. 

When  pressure  is  exerted  upon  a  solid,  on  account  of  its 
rigidity  it  is  incapable  of  transmitting  the  pressure  in  other 
than  the  direction  in  which  it  is  pressed.  With  fluids  it  is 
widely  different.  On  account  of  the  mobility  of  their  mole- 
cules, they  are  incapable  of  resisting  a  change  of  shape  when 
acted  upon  by  a  force  which  is  not  equally  applied  over  the 
whole  surface  of  the  body  of  fluid,  hence  any  force  applied 
to  a  fluid  body  must  be  transmitted  by  the  fluid  in  every 
direction.  Consequently  every  portion  of  the  interior  walls 
of  the  containing  vessel  with  which  the  fluid  is  in  contact  is 
subjected  to  pressure. 

Experiment  2. —  Measure  the  diameter  of  the  bore  of  each  arm  of  the 
glass  U-tube  (Fig.  104).  We  will  suppose,  for  illustration,  that  the 
diameters  are  respectively  40  mm  and  10  mm  ;  then  the  ratio  of  the  areas 
of  the  transverse  sections  of  the  bores  will  be  40'2 : 102=16  ;  that  is,  when 
the  tube  contains  a  liquid,  the  area  of  the  free  surface  of  the  liquid  in  the 
large  arm  will  be  16  times  as  great  as  of  that  in  the  small  arm.  Pour 
mercury  into  the  tube  until  it  stands  about  1  cm 
above  the  bottom  of  the  large  arm  as  cd.  The 
mercury  stands  at  the  same  level  in  both  arms. 
Pour  water  upon  the  mercury  in  the  large  arm  until 
this  arm  lacks  only  about  1  cm  of  being  full,  as  a  b. 
The  pressure  of  the  water  causes  the  mercury  to 
rise  in  the  small  arm,  and  to  be  depressed  in  the 
large  arm.  Pour  water  very  slowly  into  the  small 
arm  from  a  beaker  having  a  narrow  lip,  until  the 
surfaces  of  the  water  in  the  two  arms  are  at  the 

same  level.     It  is  evident  that  the  quantity  of  water  in  the  large  arm  is 
16  times  as  great  as  that  in  the  small  arm. 

This  phenomenon  appears  paradoxical  (apparently  contrary 
to  the  natural  course  of  things),  until  we  master  the  important 
hydrostatic  principle  involved.  We  must  not  regard  the  body 
of  mercury  as  serving  as  a  balance  beam  between  the  two 
bodies  of  water,  for  this  would  lead  to  the  absurd  conclusion 


144 


MOLAR    DYNAMICS. 


that  a  given  mass  of  matter  may  balance  another  mass  1.6 
times  as  great.  We  may  best  understand  this  phenomenon 
by  imagining  the  body  of  liquid  in  the  large  arm  to  be 
divided  into  cylindrical  columns  of  liquid  of  the  same  size  as 
that  in  the  small  arm.  There  will  evidently  be  16  such 
columns.  Then 'whatever  pressure  is  exerted  on  the  mercury 


FIG.  105. 

by  the  water  in  the  small  arm  is  transmitted  by  the  mercury 
to  each  of  the  16  columns,  so  that  each  column  receives  an 
upward  pressure,  or  a  supporting  force  equal  to  the  weight  of 
the  water  in  the  small  arm. 

The  pressure  exerted  by  a  fluid  upon  the  vessel  containing 
it  is  normal  to  the  walls  of  the  vessel.  Fluid  pressure  is 
expressed  by  stating  the  force  exerted  on  a  unit  area,  as  2  Ibs. 
per  sq.  in.,  5  g  per  cm2,  etc.  The  total  pressure  on  any  surface 


TRANSMISSION    OF    PRESSURE. 


145 


is  the  product  of  the  pressure  per  unit  area  multiplied  by  the 
number  of  units  of  area. 

Experiment  3.  —  Fig.  105  represents  a  section  of  an  apparatus  called 
(from  the  number  of  uses  to  which  it  may  be  put)  the  seven-in-one  appa- 
ratus. A  is  a  hollow  cylinder  closed  at  one  end.  B  is  a  tightly  fitting 
piston  which  may  be  pushed  into  or  drawn  out  of  the  cylinder  by  the 
handle  C  when  screwed  into  the  piston.  D  is  another  handle  permanently 
connected  with  the  closed  end  of  the  cylinder.  E  is  a  nipple,  opening 
into  the  space  below  the  piston.  To  this  may  be  attached  a  thick-walled 
rubber  tube  F.  G  is  a  stop-cock  and  H  is  a  funnel,  either  of  which  may 
be  inserted  at  will  into  the  free  end  of  the  tube. 

Support  the  seven-in-one  apparatus  with  the  open  end  upward,  force 
the  piston  in,  place  on  it  a  block  of  wood  A  (Fig.  106),  and  on  the  block 
a  heavy  weight.  Attach  one  end  of  the  rubber  tube 
13  (12  feet  long)  to  the  apparatus,  and  insert  a  funnel 
C  in  the  other  end  of  the  tube.  Raise  the  latter 
end  as  high  as  practicable,  and  pour  water  into 
the  tube.  Explain  how  the  few  ounces  of  water 
standing  in  the  tube  can  exert  a  pressure  of  many 
pounds  on  the  piston,  and  cause  it  to  rise  together 
with  the  burden  that  is  on  it. 


FIG.  106. 

Experiment  4.  —  Remove  the  water  from  the  apparatus,  place  on  the 
piston  a  16-pound  weight,  and  blow  (Fig.  107)  from  the  lungs  into  the 
apparatus.  Notwithstanding  that  the  actual  pushing  force  exerted 
through  the  tube  by  the  lungs  probably  does  not  exceed  a  few  ounces, 
the  slight  increase  of  pressure  caused  thereby,  when  exerted  upon  the 
(about)  26  square  inches  of  surface  of  the  piston,  causes  it  to  rise  together 
with  its  burden. 


146 


MOLAR    DYNAMICS. 


A  pressure  exerted  on  a  fluid  enclosed  in  a  vessel  is  trans- 
mitted undiminished  to  every  part  of  that  vessel  y  and  the  total 
pressure  exerted  on  the  interior  of  the  vessel  is  equal  to  the  area 
multiplied  by  the  pressure  per  unit  of  area. 

123.  The  hydraulic  press.  —  Closely  allied  to  the  seven-in- 
one  apparatus  is  the  hydraulic  press.  It  contains  two  pistons, 
t  and  s  (Fig.  108).  The  area  of  the  lower  surface  of  t  is  (say) 
one  hundred  times  that  of  the  lower  surface  of  s.  As  the 
piston  s  is  raised  and  depressed,  water  is  pumped  up  from 
the  cistern  A,  is  forced  into  the  cylinder  x,  and  exerts  an 

upward  pressure  against  the 
piston  t  one  hundred  times 
greater  than  the  downward 
pressure  exerted  upon  s. 
Thus,  if  a  pressure  of  one 
hundred  pounds  is  applied 
at  s,  the  cotton  bales  will  be 
subjected  to  a  pressure  of 
five  tons. 

The  pressure  that  may  be 
exerted  by  these  presses  is 
enormous.  The  hand  of  a 
child  can  break  a  strong  iron 
bar.  But  observe  that,  al- 
though the  pressure  exerted 
is  very  great,  the  upward  movement  of  the  piston  t  is  very 
slow.  In  order  that  the  piston  t  may  rise  1  cm,  the  piston  s 
must  descend  100  cm.  The  disadvantage  arising  from  slowness 
of  operation  is  insignificant,  however,  when  we  consider  the 
great  advantage  accruing  from  the  fact  that  one  man  can 
produce  as  great  a  pressure  with  the  press  as  a  hundred  men 
can  exert  without  it. 

The  press  is  used  for  compressing  cotton,  hay,  etc.,  into 
bales,  and  for  extracting  oil  from  seeds.  The  modern  engineer 


FIG.  108. 


PRESSURE   OF    FLUID   DUE   TO    ITS   WEIGHT.        147 

finds  it  a  most  efficient  machine  whenever  great  resistances 
are  to  be  moved  through  short  distances. 

124.  Pressure  of  fluid  due  to  its  weight.  —  Fluids  exert 
pressure  due  to  their  weight.  Imagine  a  vessel  filled  with 
shot ;  you  will  understand  that  the  upper  layer  of  shot  will 
press  upon  the  layer  next  beneath  with  a  force  equal  to  its 
weight,  the  second  upon  the  third  with  a  force  equal  to  the 
sum  of  the  weights  of  the  first  two,  and  so  on.  You  will  also 
readily  conclude  that  the  pressure  exerted  upon  the  successive 
layers  will  be  exactly  proportional  to  their  depths,  unless  in 
consequence  of  the  great  pressure  to  which  the  lowest  layers 
are  subjected  there  should  be  a  crowding  together  of  the  shot 
so  as  to  make  them  more  compact.  In  this  case  there  would 
be  a  slight  variation  from  the  rule  as  stated.  For  a  like  reason 
the  downward  pressure  in  a  body  of  liquid  increases  as  its 
depth  except  in  so  far  as  the  pressure  is  modified  in  conse- 
quence of  the  compressibility  of  liquids.  Liquids  are,  how- 
ever, so  slightly  compressible  that  any  variation  in  conse- 
quence of  the  compression  is  usually  neglected,  and  the 
principle  is  stated  in  general  that  pressure  at  any  point  in  a 
liquid  varies  as  its  depth. 

Since  the  shot  possess  a  certain  degree  of  mobility  or  free- 
dom of  motion  around  one  another,  their  weight  will  cause  to 
some  extent  a  lateral  pressure  against  one  another  and  against 
the  walls  of  the  con- 
taining vessel, 
consequence  of 
extreme  mobility  of 
the  molecules  of  fluids  | 
the  downward  pres-  g 
sure  due  to  gravita-  ' 
tion  at  any  point  in  FlG-  1Q9- 

a  fluid  gives  rise  to  an  equal  pressure  at  that  point  in  all 
directions.  Hence  the  so-called  Pascal's  principle :  At  any 
point  in  a  fluid  at  rest  the  pressure  is  equal  in  all  directions. 


148 


MOLAR    DYNAMICS. 


Thus,  let  a,  b,  c,  etc.  (Fig.  109),  represent  imaginary  surfaces, 
and  the  arrow-heads  the  direction  of  pressure  exerted  at 
points  in  these  surfaces  at  equal  depths  in  a  liquid.  The 
pressures  exerted  at  these  several  points  are  equal. 

The  truth  of  this  principle  is  obvious,  for  if  there  be  any 
inequality  of  pressure  at  any  point,  the  unbalanced  force  will 
cause  particles  at  that  point  to  move,  which  is  contrary  to  the 
supposition  that  the  fluid  is  at  rest.  Conversely,  when  there 
is  motion  in  a  body  of  fluid  it  is  evidence  of  an  inequality 
of  pressure. 

125.  Methods  of  calculating  liquid  pressure.  —  Conceive  of 
a  square  prism  of  water  (Fig.  110),  in  the  midst  of  a 
body  of  water,  its  upper  surface  coinciding  with  the  free 

surface  of  the  liquid.  Let 
the  prism  be  4  cm  deep  and 
1  cm  square  at  the  end  ;  then 
the  area  of  one  of  its  ends  is 
1  cm2  and  the  volume  of  the 
prism  is  4  cc.  Xow  the  weight 
of  4  cc  of  water  is  4  g,  hence 
this  prism  must  exert  a 
downward  pressure  of  4  g 
upon  an  area  of  1  cm2.  But 
at  the  same  depth  the  pres- 
sure in  all  directions  is  the 
same,  hence,  generally,  the 
pressure  at  any  depth  in 
water  may  be  taken  approxi- 
mately as  one  gram  per 
square  centimeter  for  each 
centimeter  of  depth  (=c=  1,000k  per  m2  for  each  meter  of 
depth;  or,  since  the  weight  of  water  is  about  62.3  Ibs.  per 
cu.  ft.,  the  pressure  is  62.3  Ibs.  per  square  foot  for  each  foot 
of  depth).  In  any  other  liquid,  to  determine  the  pressure  at 


FIG.  no. 


METHODS    OF    CALCULATING    LIQUID    PRESSURE.    149 

any  depth  the  water  pressure  at  the  given  depth  must  be 
multiplied  by  the  specific  density  (p.  177)  of  the  liquid. 

The  conclusions  arrived  at  may  be  summarized  as  follows : 
In  a  mass  of  liquid  at  rest,  the  pressure  is  the  same  at  all  points 
in  any  horizontal  plane,  and  is  equal  to  the  weight  of  a  column 
of  the  liquid  one  square  centimeter  in  section  extending  vertically 
from  the  horizontal  plane  to  a  horizontal  plane  coinciding  with 
the  upper  surface  of  the  liquid. 

Experiment  5.  —  Take  a  square  prism  of  pine  wood  1  cm  square  at 
its  ends.  Find  its  weight  in  grams  and  calculate  to  what  depth  it  would 
sink  endwise  in  water.  Take  a  test  tube  a  little  larger  and  longer  than 
the  prism.  Nearly  fill  the  tube  with  water,  lower  the  prism  into  the 
water,  and  verify  your  calculation.  How  great  is  the  upward  pressure  of 
the  water  upon  the  bottom  of  the  prism  ? 


FIG.  112. 


FIG.  us. 


FIG.  114. 


Experiment  6.  — A  and  B  (Fig.  Ill)  are  two  bottomless  vessels  which 
can  be  alternately  screwed  to  a  supporting  ring  C  (Fig.  112).  The  ring 
is  itself  fastened  by  means  of  a  clamp  to  the  rim  of  a  wooden  waterpail. 


150  MOLAR   DYNAMICS. 

A  circular  disk  of  metal  D  is  supported  by  a  rod  connected  with  one 
arm  of  the  balance-beam  E.  When  the  weight  F  is  applied  to  the  other 
arm  of  the  beam,  the  disk  D  is  drawn  up  against  the  ring  so  as  to  supply 
a  bottom  for  the  vessel  above.  Take  first  the  vessel  A,  screw  it  to  the 
ring  and  apply  the  weight  to  the  beam  as  in  Fig.  114.  Pour  water  slowly 
into  the  vessel,  moving  the  index  a  up  the  rod  so  as  to  keep  it  just  at  the 
surface  of  the  water,  until  the  downward  pressure  of  the  water  upon  the 
bottom  tilts  the  beam,  and  pushes  the  bottom  down  from  the  ring,  and 
allows  some  of  the  water  to  fall  into  the  pail.  Remove  vessel  A,  and 
attach  B  to  the  ring  as  in  Fig.  113.  Pour  water  as  before  into  vessel  B  ; 
when  the  surface  of  the  water  reaches  the  index  a,  the  bottom  is  forced 
off  as  before. 

That  is,  the  pressures  upon  the  bottoms  of  all  vessels  (of  whatever 
capacity  or  shape)  are  the  same,  provided  the  bottoms  be  of  the  same  area 
and  the  depth  and  density  of  the  liquid  be  the  same. 

126.  Rules  for  calculating  liquid  pressure  against  the  bottom 
and  sides  of  a  containing  vessel.  —  The  total  pressure  due  to 
gravity  on  any  portion  of  the  horizontal  bottom  of  a  vessel  con- 
taining a  liquid  is  equal  to  the  iv  eight  of  a  column  of  the  same 
liquid  whose  base  is  the  area  of  that  portion  of  the  bottom  pressed 
upon,  and  whose  hight  is  the  depth  of  the  water  in  the  vessel. 
Thus,  suppose  that  we  have  three  vessels  having  bottoms  of  the 
same  size :  one  of  them  has  flaring  sides,  like  a  wash-basin ; 
another  has  cylindrical  sides  ;  and  the  third  has  conical  sides, 
like  a  coffee-pot.  If  the  three  vessels  be  filled  with  water  to 
the  same  depth,  the  total  pressure  upon  the  bottom  of  each 
will  be  equal  to  the  weight  of  the  water  in  the  vessel  of 
cylindrical  shape.  Suppose  that  the  area  of  the  bottom  of 
each  is  108  square  inches,  and  the  depth  of  water  is  16  inches  ; 
then  the  cubical  contents  of  the  water  in  the  cylindrical  vessel 
is  1,728  cubic  inches,  or  1  cubic  foot.  The  weight  of  1  cubic 
foot  of  water  is  62.3  pounds.  Hence,  the  total  pressure  upon 
the  bottom  of  each  vessel  is  62.3  pounds. 

Evidently,  the  lateral  pressure  at  any  point  of  the  side  of 
a  vessel  depends  upon  the  depth  of  that  point ;  and,  as  depth 
at  different  points  of  a  side  varies,  to  find  the  total  pressure 


SUKFACE   OF   A    LIQUID   AT    REST   IS   LEVEL.        151 

upon  any  portion  of  a  side  of  a  vessel,  find  the  weight  of  a 
column  of  liquid  whose  base  is  the  area  of  that  portion  of  the 
side,  and  whose  hight  is  the  average  depth  of  that  portion. 

127.  The  surface  of  a  liquid  at  rest  is  level.  — By  jolting  a 
vessel  the  surface  of  a  liquid  in  it  may  be  made  to  assume  the 
form  seen  in  Fig.  115.  Can  it  retain  this  form  ?  Take  two 
molecules  of  the  liquid  at  the  points  a  and  b  on  the  same  level. 
The  total  downward  pressures  upon  a  and  b  are 
as  their  respective  depths  ca  and  db.  But 
since  (assuming  the  mass  of  liquid  to  be  at  rest) 
the  pressure  at  a  given  depth  is  equal  in  all 
directions,  c  a  and  d  b  represent  the  lateral  pres- 
sures at  the  points  a  and  b  respectively.  But 
db  is  greater  than  ca  ;  hence,  the  molecules  a  and  b,  and  those 
lying  in  a  straight  line  between  them,  are  acted  upon  by  two 
unequal  forces  in  opposite  directions.  Hence  the  liquid  can- 
not be  at  rest  in  the  position  assumed  and  there  will,  therefore, 
be  a  movement  of  molecules  in  the  direction  of  the  greater 
force,  toward  a,  till  there  is  equilibrium  of  forces,  which  will 
occur  only  when  the  points  a  and  b  are  equally  distant  from 
the  surface ;  or,  in  other  words,  there  will  be  no  rest  till  all 
points  in  the  surface  are  on  the  same  level. 

This  fact  is  commonly  expressed  thus  :  ' '  Water  always  seeks  its 
lowest  level."  In  accordance  with  this  principle,  water  flows  down 
an  inclined  plane,  and  will  not  remain  heaped  up.  An  illustration 
of  the  application  of  this  principle,  on  a  large  scale,  is  found  in  the 
method  of  supplying  cities  with  water.  Fig.  116  represents  a  modern 
aqueduct,  through  which  water  is  conveyed  from  an  elevated  pond 
or  river  a,  beneath  a  river  6,  over  a  hill  c,  through  a  valley  d,  to  a 
reservoir  e,  from  which  water  is  distributed  by  service-pipes  to  the 
dwellings  in  a  city.  The  pipe  is  tapped  at  different  points,  and 
fountains  would  rise  to  the  level  of  the  water  in  the  pond  were  it 
not  for  the  resistance  of  the  air  and  the  check  which  the  ascending 
stream  receives  from  the  falling  drops.  Where  should  the  pipes  be 
made  stronger,  on  a  hill  or  in  a  valley  ?  Where  will  water  issue 


152 


MOLAR    DYNAMICS. 


from  faucets  with  greater  force,  in  a  chamber  or  in  a  basement  ? 
How  high  may  water  be  drawn  from  the  pipe  in  the  house/? 

128.    Artesian  wells,  etc.  —  In  most  places,  the  crust  of  the  earth 
is  composed  of  distinct  layers  of  earth  and  rock  of  various  kinds. 


FIG.  no. 


These  layers  frequently  assume  concave  shapes,  so  as  to  resemble 
cups  placed  one  within  another.  Fig.  117  represents  a  vertical 
section  exposing  a  few  of  the  surface-layers  of  the  earth's  crust : 
a  is  a  stratum  of  loose  sand  or  gravel ;  6,  a  clay -bed  ;  c,  a  stratum 


FIG.  117. 

of  slate ;  d,  a  stratum  of  limestone ;  the  whole  resting  on  a  bed  of 
granite  e.  If  you  hollow  out  a  lump  of  clay,  and  pour  water  into 
the  cavity,  you  will  find  that  the  water  will  percolate  through  the 
clay  very  slowly.  Water  that  falls  in  rain  passes  readily  through 
the  gravel  a,  till  it  reaches  the  clay-bed  b,  where  it  collects.  Hence 
a  well  sunk  to  the  clay-bed,  will  fill  with  water  as  high  as  the  water 


ARTESIAN    WELLS. 


153 


stands  above  the  clay.  Water  also  works  its  way  from  elevated 
places  down  between  the  strata  of  rocks.  If  a  hole  be  bored 
through  the  slate  c,  water  will  rise  above  the  surface  of  the  ground 
in  a  fountain,  seeking  the  level  of  its  source  on  the  hill ;  and  if  bored 
still  lower,  through  the  stratum  cZ,  a  still  higher  fountain  may  result. 
Such  borings  are  called  Artesian  wells.  Water  frequently  forces 
its  way  through  fissures  in  the  rocky  strata  to  the  surface,  as  at  t, 
and  gives  rise  to  springs. 


Exercises. 

1  1.  The  areas  of  the  bottoms  of  vessels  A,  B,  and  C  (Fig.  118)  art- 
equal.  The  vessels  have  the  same  depth,  and  are  filled  with  water. 
Which  vessel  contains  the  most  water  ?  On  the  bottom  of  which  vessel 
is  the  pressure  equal  to  the  weight  of  the  water  which  it  contains  ?  How 
does  the  pressure  upon 
the  bottom  of  vessel 
B  compare  with  the 
weight  of  the  water 


J.BJ     I 
FIG. 118. 


Q      C 


in  it? 

,   2.    A  cubic   foot  of 

water     weighs     about 

02.3  pounds  or  1000  ounces.     Suppose  that  the  area  of  the  bottom  of 

each  vessel  is  100  square  inches  and  the  depth  is  10  inches ;  what  is  the 

pressure  on  the  bottom  of  each  ? 

3.  Vessel  A  is  a  cubical  vessel ;  what  is  the  total  pressure  against  one 
of  its  vertical  sides  ? 

v  4.  Suppose  that  vessel  A  were  tightly  covered,  and  that  a  tube  10  feet 
long  were  passed  through  a  perforation  in  the  cover  so  that  the  end 
should  just  touch  the  upper  surface  of  the  water  in  the  vessel ;  then  sup- 
pose the  tube  to  be  filled  with  water.  What  additional  pressure  would 
each  wall  of  the  cube  sustain  ? 

5.  Suppose  that  the  area  of  the  end  of  the  large  piston  of  a  hydraulic 
press  is  100  square  inches  ;  what  should  be  the  area  of  the  end  of  the 
small  piston  that  a  force  of  100  pounds  applied  to  it  may  produce  a  pres- 
sure of  2  tons  ? 

[Exercises  6  to  10  inclusive  should,  if  practicable,  be  actually  per- 
formed in  the  manner  directed,  either  by  the  students  individually,  or  by 
one  or  two  members  of  the  class  in  the  presence  of  the  rest,  while  all 
work  out  the  results  from  the  data  thus  obtained.] 


154 


MOLAR   DYNAMICS. 


FIG.  119. 


v  6.  Take  a  glass  U-tube  (Fig.  119)  about  40  in.  high,  having  a  stout 
rubber  tube  a  attached,  and  containing  mercury  with  the  surfaces  at  the 
same  level  in  both  arms.  a.  Blow  into  the  tube ;  the 
surfaces  of  mercury  will  at  once  assume  different 
levels.  How  will  you  determine  the  pressure  which 
you  exert  through  the  air  in  the  tube  upon  the  mer- 
cury (the  specific  density  of  mercury  being  13. 59)  ? 

7.  a.  Suck  air  from  a  ;  what  happens  to  the  mer- 
cury ?     &.  How  will  you  determine  the  diminution  of 
pressure  which  you  produce  by  suction  ? 

8.  Take  a  similar  tube  containing  water  instead  of 
mercury,  connect  it  with  a  gas  jet,  and  turn  on  the 

gas ;  how  would  you  determine  how  much  greater  (or  less)  its  pressure 
is  than  that  of  the  atmosphere  ? 

9.  a.  Having  ascertained  as  in  Exercise  7. -the  greatest  pressure  you 
can  exert  by  blowing,  how  would  you  proceed  to  determine  the  greatest 
weight,  placed  on  the  piston  of  the  seven-in-one  apparatus  (Fig.  120),  that 
you  could  support,  provided  there  were  no  friction  and  the  apparatus 
were  perfectly  air-tight  ?    b.  How  would  you  estimate 

the  loss  in  force  in  consequence  of  friction,  etc.  ? 

10.  If  the  apparatus  be  inverted  and  a  weight  be 
hung  from  the  piston,  as  in  Fig.  120,  how  would  you 
determine  the  greatest  weight  you  ought  to  be  able  to 
raise  by  suction  ? 

11.  How  great  is  the  hydrostatic  pressure  in  fresh 
water  at  the  depth  50  feet  ? 

—12.  Why  does  not  a  person  who  dives  to  the  bottom 
of  a  pond  feel  the  weight  of  the  column  of  water  above 
him? 

13.  Why  does  not  the  weight  of  the  greater  quan- 
tity of  liquid  in  a  coffee  pot  when  filled  cause  the 
liquid  to  rise  higher  in  -the  spout  than  the  surface  of 
the  liquid  in  the  pot  ? 

-14.  a.  A  house  is  supplied  with  water  by  a  system  of  pipes  from  a 
distant  reservoir,  as  is  customary  in  cities  ;  what  data  would  you  require 
in  order  to  compute  the  pressure  at  any  point  in  the  pipe  ?  6.  How 
much  greater  is  the  pressure  at  a  point  in  the  pipe  in  the  cellar  than  at 
another  point  in  the  attic  ?  c.  Is  the  pressure  in  the  pipe  the  same  when 
water  is  running  from  a  faucet  in  the  house  as  when  the  water  is  at 
rest?  Why? 


FIG.  120. 


ATMOSPHERIC   PRESSURE.  155 

15.  A  (Fig.  121)  represents  a  stand-pipe  for  furnishing  the  neighboring 
district  with  water  by  the  action  of  gravity.  The  stand-pipe  is  supplied 
with  water  from  a  lake  in  the  vicinity  by  means  of  a  pumping  engine. 


FIG.  121. 

Vertical  distances  are  represented  on  a  scale  of  £  in.  =s=  50  ft.  If  the 
stand-pipe  be  filled  to  the  level  m  n  and  the  water  be  at  rest  in  the 
main  pipe  leading  from  it,  what  pressure  will  the  pipe  sustain  at  points 
a,  c,  and  d  respectively  ? 

SECTION  II. 

ATMOSPHERIC    PRESSURE. 

129.  Introduction.  —  We  live  at  the  bottom  of  an  exceed- 
ingly rare  and  elastic  aerial  ocean,  called  the  atmosphere, 
extending  to  an  undetermined  distance  into  space.  Every 
molecule  in  the  gaseous  ocean  is  drawn  towards  the  earth's 
center  by  gravitation  and  the  atmosphere  is  thus  bound  to  the 
earth  by  this  force,  just  as  is  the  liquid  ocean.  Evidently  the 
pressure  in  the  atmosphere  due  to  its  weight  increases  with 
the  depth  ;  or,  since  in  our  position  we  are  more  accustomed 
to  speak  of  hight  in  the  atmosphere,  decreases  with  the  hight. 
The  pressure  does  not  diminish  regularly  with  the  hight  as 
in  an  ocean  of  incompressible  fluid.  Air  is  very  compressible 
and  therefore  varies  in  density.  The  lower  strata  of  air 
sustaining  the  weight  of  air  above  are  relatively  much  com- 
pressed, very  dense,  and  elastic.  The  density  and  elasticity 
of  the  air  diminish  more  rapidly  than  the  hight  above  sea- 
level  increases.  Owing  to  this  fact  the  greater  part  of  the 


156 


MOLAR    DYNAMICS. 


mass  of  the  atmosphere  is  within  three  and  a  half  miles  of 
the  sea-level  (see  Fig.  132).  Above  this  hight  the  air  is 
much  rarefied  and  vanishes,  as  it  were,  very  gradually  into 
empty  space. 

Experiment  1.  —  Fill  two  glass  jars  (Fig.  122)  with  water,  A  having  a 
glass  bottom,  B  a  bottom  provided  by  tying 
a  piece  of  sheet-rubber  tightly  over  the  rim. 
Invert  both  in  a  larger  vessel  of  water,  C. 
The  water  in  A  does  not  feel  the  downward 
pressure  of  the  air  directly  above  it,  the 
pressure  being  sustained  by  the  rigid  glass 
bottom.  But  it  indirectly  feels  the  pressure 
of  the  air  on  the  surface  of  the  water  in  the 
open  vessel,  and  it  is  this  pressure  that  sustains 
the  water  in  the  jar.  But  the  rubber  bottom 
of  the  jar  B  yields  somewhat  to  the  down- 
ward pressure  of  the  air,  and  is  forced  inward. 
Experiment  '2. — Fill  a  glass  tube,  D,  with  water,  keeping  the  lower 

end  in  a  vessel  of  water,  and  the  upper  end 

tightly  closed  with  a  finger.     Why  does  not 

the  water  in  the  tube  fall  ?     Remove  your 

finger  from  the  closed  end.     Why  does  the 

water  fall  ? 

Experiment  3.  —  Fill   (or  partly  fill)   a 

tumbler  with  water,  cover  the  top  closely 

with  a  card    or  writing-paper,    hold    the 

paper  in  place  with  the  palm  of  the  hand, 

and  quickly  invert  the  tumbler  (Fig.  123). 

Why  does  not  the  water  fall  out  ? 

Experiment  4.  —Force  the  piston  A  (Fig. 

124)  of  the  seven-in-one  apparatus  quite  to 

the  closed  end  of  the  hollow  cylinder,  and 

close  the  stop-cock  B.     Try  to  pull  the  piston  out  again. 

not  succeed  ? 


122. 


FIG.  123. 


Why  do  you 
Hold  the  apparatus  in 
various  positions,  so  that  the  atmosphere 
may  press  down,  laterally,  and  up, 
against  the  piston.  Do  you  discover 
any  difference  in  the  pressure  which  it 
receives  from  different  directions  ? 


FIG.  124. 


HOW    ATMOSPHERIC    PKESSUKE    IS    MEASURED.     157 


130.    How  atmospheric  pressure  is  measured. 

Experiment  5  (preliminary). —Take  a  U-shaped  glass  tube  (Fig.  125), 
half  fill  it  with  water,  close  one 
end  with  a  thumb,  and  tilt  the 
tube  so  that  the  water  will  run 
into  the  closed  arm  and  fill  it ; 
then  restore  it  to  its  original  ver- 
tical position.  Why  does  not  the 
water  settle  to  the  same  level  in 
both  arms  ? 


FIG.  125. 


Fig.  126  represents  a  U-shaped  glass  tube  closed  at  one 
end,  34  inches  in  hight,  and  with  a  bore  of 
1  square  inch  section.  The  closed  arm  hav- 
ing been  filled  with  mercury,  the  tube  is 
placed  with  its  open  end  upward,  as  in  the 
cut.  The  mercury  in  the  closed  arm  sinks 
about  2  inches  to  A,  and  rises  2  inches  in 
the  open  arm  to  C  ;  but  the  surface  A  is  30 
inches  higher  than  the  surface  C.  This  can 
be  accounted  for  only  by  the  atmospheric 
pressure.  The  column  of  mercury  B  A,  con- 
taining 30  cubic  inches,  is  an  exact  coun- 
terpoise for  a  column  of  air  of  the  same 
diameter  extending  from  C  to  the  upper 
limit  of  the  atmospheric  ocean,  —  an  un- 
known hight. 

The  weight  of  the  30  cubic  inches  of  mer- 
cury in  the  column  B  A  is  about  14.7  pounds. 
Hence  the  weight  of  a  column  of  air  of  1  square-inch  section, 
extending  from  the  surface  of  the  sea  to  the  upper  limit  of 
the  atmosphere,  is  about  14.7  pounds.  But  in  fluids  gravity 
causes  equal  pressure  in  all  directions.  Hence,  at  the  level 
of  the  sea,  all  bodies  are  pressed  upon  in  all  directions  bi/  the 
atmosphere,  with  a  force  of  about  14.7  pounds  per  square  inch, 
or  about  one  ton  per  square  foot. 


FIG.  12G. 


158 


MOLAR    DYNAMICS. 


A  pressure  of  15  pounds  per  square  inch  is  quite  generally 
adopted  by  engineers  as  a  unit  of  gaseous  pressure,  and  is 
called  an  atmosphere.  Physicists,  however,  generally  measure 
pressure  in  terms  of  cm  or  mm  of  mercury  at  0°  C. ;  that  is, 
the  hight  in  mm  of  mercury  that  the  pressure  of  the  atmos- 
phere sustains  in  the  tube. 


ESE! 


FIG.  127. 

131.  The  barometer.  —  The  hight  of  the  col- 
umn of  mercury  supported  by  atmospheric  pres- 
sure is  quite  independent  of  the  area  of  the 
surface  of  the  mercury  pressed  upon  ;  hence  the 
apparatus  is  more  conveniently  constructed  in 
the  form  represented  in  Fig.  127. 

A  straight  tube  about  34  inches  long  is  closed 
at  one  end  and  filled  with  mercury.  The  tube  is 
inverted,  with  i$s  open  end  tightly  covered  with 
a  finger,  and  this  end  is  inserted  into  a  vessel  of 
mercury.  When  the  finger  is  withdrawn  the 


FIG.  128. 


THE   FORTIN    BAROMETER. 


159 


mercury  sinks  until  there  is  equilibrium  between  the  down- 
ward pressure  of  the  mercurial  column  AB  and  the  pressure 
of  the  atmosphere.  The  empty  space  at  the  top  of  the  tube 
is  called  a  Torricellian x  vacuum.  An  apparatus  designed  to 
measure  atmospheric  pressure  is  called  a  barometer  (pressure- 
measurer).  A  common  cheap  form  of  barometer  is  repre- 
sented in  Fig.  128.  Beside  the  tube  and  near  its  top  is  a 
scale  graduated  in  inches  or  centimeters,  indicating  the  hight 
of  the  mercurial  column.  For  ordinary  purposes  this  scale 
needs  to  have  a  range  of  only  three  or  four  inches,  so  as  to 
include  the  maximum  fluctuations  of  the  column.2 

132.  The  Fortin  barometer.  —  We  will  suppose  the  scale  of  a 
barometer  to  be  fixed  so  as  to  indicate  correctly  the  hight  of  the 
surface  of  mercury  in  the  tube  above  that  in  the 
cistern  at  a  time,  for  instance,  when  this  distance 
is  30  inches.  A  point  on  the  surface  of  the  mercury 
in  the  cistern  in  this  case  is  called-  technically  the 
zero  point.  Now  should  the  mercury  fall  in  the 
tube  to  29  and  the  mercury  in  the  cistern  remain 
at  zero,  then  the  scale  reading  would  indicate 
correctly  the  barometric  hight;  but  the  mercury 
does  not  remain  at  zero,  but  rises  a  little  (less  as 
the  diameter  of  the  cistern  is  greater),  consequently 
the  scale-reading  is  too  great.  When  the  mercury 
is  higher  in  the  tube  than  30  all  the  readings  will 
be  too  small.  Evidently,  then,  the  mercury  in  the 
cistern  must  be  brought  to  zero  at  every  obser- 
vation in  order  to  eliminate  this  error.  This  is 
easily  accomplished  with  the  Fortin  barometer. 
The  bottom  of  the  cistern  of  this  barometer  is 
pliable  leather  resting  on  a  thumb-screw  A  (Fig. 
129).  Projecting  from  the  tube  inside  of  the  cistern 
is  a  little  pointer  B  of  colored  glass.  The  lower  end 
of  this  pointer,  called  the  fiducial  point,  corresponds 
to  the  zero  point.  The  level  of  the  mercury  in  the 
cistern  must  be  set  to  this  point  by  raising  or  FlG  129 

1  The  first  barometer  was  constructed  by  Torricelli,  a  Florentine,  in  1643. 

2  At  the  Central  Station  in  Boston,  Feb.  8,  1895,  the  mercury  fell  to  28.61  in.,  the 
lowest  on  record  at  this  station.     The  highest  point  attained  at  this  station  Avas  30.97 
in.  on  Dec.  1, 1887,  and  Dec.  31,  1889. 


160 


MOLAR    DYNAMICS. 


lowering  the  cistern  base  by  the  adjusting  screw,  before  taking  a 
reading.  A  sliding  piece  C,  Fig.  130,  furnished  with  a  vernier1 
can  be  slid  along  the  tube  so  as  to  enable  one  to  read  with  great 
accuracy. 

In  refined  scientific  researches  it  is  necessary  to  make  suitable 
allowances  for  expansion  and  contraction  of  the  mercury  attending 
changes  in  temperature,  hence   a  very  sensitive  ther- 
mometer is  attached  to  the  barometer.     Also  allowances 
for  capillary  depression  must  be  made. 

133.  The  aneroid  barometer.  —  The  aneroid  (without 
moisture)  barometer  employs  no  liquid.  Tt  contains  a 
cylindrical  box,  D  (Fig.  131),  having  a  very  flexible  top. 
The  air  is  partially  exhausted  from  within  the  box.  The 
varying  atmospheric  pressure  causes  this  top  to  rise  and 
sink  much  like  the  chest  of  a  man  in  breathing.  Slight 
movements  of  this  kind  are  communicated  by  means  of 
multiplying-apparatus  (apparatus  by  means  of  which  a 
small  movement  of  one  part  causes  a  large  movement  of 
FIG  130  another  part)  to  .the  index  needle  A.  The  dial  is  gradu- 
ated to  correspond  with  a  mercurial  barometer.  The 

observer  turns  the  button  C  and  brings  the  brass  needle  B  over  the 

black   needle   A,  and   at  his   next 

observation   any   departure   of  the 

latter  from  the  former  will  show  pre- 
cisely the  change  which  has  occurred 

between  the  observations. 

The  aneroid  can  be  made  more 

sensitive  (i.e.  so  as  to  show  smaller 

changes    of   atmospheric    pressure) 

than     the     mercurial     barometer. 

Owing  to  this  as  well  as  to  its  con- 
venient   size    and    portability,    the 

aneroid  has  become  quite  popular. 

Unfortunately,  however,  it  does  not 

preserve   its  accuracy    for  a  great 

length  of  time,  hence  it  must  be  adjusted  from  time  to  time  to  a 

standard  mercurial  barometer. 


FIG.  131. 


1  For  construction  and  methods  of  using  verniers  the  student  is  referred  to 
Pickering's  "  Manual  of  Physical  Manipulations,"  or  Stewart  and  Gee's  "  Elementary 
Practical  Physics." 


STANDARD    PRESSURE.  161 

134.  Standard  pressure.  —  Many  physical  operations  require 
a  standard  pressure  for  reference.     The  standard  generally 
adopted  is  the  pressure  exerted  by  a  column  of  pure  mercury 
at  0°  C.  and  76  cm.  (29.922  inches)  high,  which  is  about  the 
average  hight  of  the  barometric  column  at  sea-level  in  latitude 
45°.      The  pressure  corresponding   to   this  hight  is   1033.3 
grams   per   square   centimeter  or   14.69  pounds    per   square 
inch. 

135.  Barometric  measurement  of  hights.  —  Since  atmospheric 
pressure  varies  with  the  hight  above  sea-level,  it  is  evident 
that  changes  in  elevation  may  be  determined  from  changes 
of  pressure  as  indicated  by  the  barometer.     In  other  words, 
the  hight  of  a  mountain  may  be  ascertained  from  barometric 
readings  made  on  the  summit  and  at  sea-level.     Such  deter- 
minations are  more  reliable  for  moderate  elevations,  as  there 
are  elements  of  greater  or  less  uncertainty  in  measuring  great 
hights.     For  moderate  hights  the  barometric  column  falls  at 
a  very  nearly  uniform  rate  of  one  inch  for  every  900  feet  of 
ascent. 

If  a  mercurial  barometer  stand  at  760  mm.  on  the  floor,  the 
same  barometer  on  the  top  of  a  table  1  m.  high  should  stand 
at  a  hight  of  759.91  mm.,  a  change  scarcely  perceptible.  The 
aneroid  is,  however,  sometimes  made  so  sensitive  that  the 
change  of  pressure  experienced  in  this  short  distance  is  ren- 
dered quite  perceptible. 

The  shading  in  Fig.  132  is  intended  to  indicate  roughly  the 
variation  in  the  density  of  the  air  at  different  elevations  above 
sea-level.  The  figures  in  the  left  margin  show  the  hight  in 
miles  ;  those  in  the  first  column  on  the  right,  the  corresponding 
average  hight  of  the  mercurial  column  in  inches ;  and  those 
in  the  extreme  right,  the  density  of  the  air  compared  with  its 
density  at  sea-level. 

It  is  calculated  that  if  an  opening  could  be  made  in  the 
earth  35  miles  in  depth  below  the  sea-level,  the  density  of  the 


162 


MOLAR    DYNAMICS. 


air  at  the  bottom  would  be  1,000  times  that  at  sea-level,  so 
that  water  would  float  in  it. 


15 


FIG.  132. 

If  the  aerial  ocean  were  of  uniform  density,  and  of  the  same 
density  that  it  is  at  sea-level,  its  depth  would  be  a  little  less 
than  live  miles.  Only  a  few  peaks  of  the  Himalayas  would 
rise  above  it. 

136.  The  barometer  in  meteorology.1  —  The  barometer  is  some- 
times called  a  "weather-glass,"  chiefly  because  its  scale  frequently 
bears  the  words  /air,  rainy,  'storm,  etc.  These  words  are  very 
objectionable,  since  they  are  totally  wrong  from  a  meteorological 
point  of  view.  To  form  a  forecast  of  the  weather  of  much  value,  a 

1  The  following  works  will  be  found  useful  to  students  of  meteorology :  "  Ele- 
mentary Meteorology,"  by  W.  M.  Davis  ;  "  Instructions  in  the  Use  of  Meteorological 
Instruments,"  "Elementary  Meteorology,"  "  Weather  Charts  and  Storm  Warnings," 
by  R.  H.  Scott;  "Weather  Casts  and  Storm  Prevision,"  by  R  Strachan;  and  "A 
Treatise  on  Meteorological  Instruments,"  by  Negretti  and  Zambra. 


THE   BAROMETER   IN   METEOROLOGY.  163 

barometer,  a  thermometer,  and  a  hygrometer  must  be  consulted, 
and  one  must  be  familiar  with  the  laws  which  govern  the  relations 
between  atmospheric  pressure,  temperature,  moisture,  etc.  In 
forming  a  judgment  of  forthcoming  weather,  the  point  at  which  the 
mercury  stands  should  not  be  so  much  regarded  as  whether  it  is 
rising  or  falling.  The  following  general  rules  may  not  be  amiss, 
though  even  these  have  many  exceptions  :  — 

1.  A  steady  barometer  at  about  its  mean  hight,  with  a  seasonable 
temperature,  and  dry  air,  indicates  a  continuation  of  fine  weather. 

2.  A  rise  from  this  point  indicates  decidedly  fine  and  dry  ;  a  fall 
indicates  rain  or  higher  wind. 

3.  A  gradual  rise  or  fall  indicates  a  less  immediate  change  than 
a  more  rapid  motion  of  the  mercury. 

Fluctuations  in  barometric  pressure  are  of  hourly  occurrence. 
Some  of  the  many  conditions  which  influence  the  atmospheric  pres- 
sure are  the  following  :  (1)  Temperature.  A  rise  of  temperature 
tends  to  diminish  the  air-pressure.  In  general  the  barometer  falls 
as  the  thermometer  rises.  Heat  expands  the  air,  causing  a  lateral 
flow  away  from  the  heated  areas.  (2)  Humidity.  Moist  air  is 
lighter  than  dry  air  having  an  equal  pressure.  (3)  Currents  in  the 
atmospheric  ocean.  On  weather  charts,  lines  called  isobars  are  drawn 
through  places  having  the  same  pressure.  Frequently  the  isobar 
indicating  the  lowest  pressure  encloses  an  area  more  or  less  circular. 
This  is  called  a  "  center  of  depression."  The  surrounding  air  tends 
to  flow  into  it  from  all  sides.  The  greater  the  difference  of  pressure 
between  the  two  places,  i.e.  the  steeper  the  barometric  gradient, 
the  more  rapid  the  flow.  The  direction  of  the  wind,  however,  is  so 
modified  by  the  rotation  of  the  earth  that  the  flow  is  not  directly 
toward  the  center,  but  spirally  toward  it,  the  motion  in  the  northern 
hemisphere  being  opposite  to  the  direction  in  which  the  hands  of  a 
watch  move. 


164 


MOLAR   DYNAMICS. 


-    SECTION    III. 


RELATION  BETWEEN  THE  DENSITY,  VOLUME,  AND  PRESSURE 
OF  A  BODY  OF  GAS. 

137.    Boyle 's  (or  Mariotte's)  Law. 

Experiment  1.  —Take  a  bent  glass  tube  (Fig.  133),  the  short  arm  being 
^^  closed,  and  the  long  arm,  which  should  be  at  least  34 

inches  (85cm.)  long,  being  open  at  the  top.  Pour 
mercury  into  the  tube  till  the  surfaces  in  the  two 
arms  stand  at  zero.  Now  the  surface  in  the  long 
arm  supports  the  pressure  of  an  atmosphere.  There- 
fore the  pressure  of  the  air  enclosed  in  the  short  arm, 
which  exactly  balances  it,  must  be  about  15  pounds 
to  the  square  inch.  Next  pour  mercury  into  the  long 
arm  till  the  surface  in  the  short  arm  reaches  5,  or  till 
the  volume  of  air  enclosed  is  reduced  one  half,  when 
it  will  be  found  that  the  hight  of  the  column  A  C  is 
just  equal  to  the  hight  of  the  barometric  column  at 
the  time  the  experiment  is  performed.  It  now  ap- 
pears that  the  pressure  of  the  air  in  A  B  balances  the 
atmospheric  pressure,  plus  a  column  of  mercury  A  C 
which  is  equal  to  another  atmosphere  ;  .-.  the  pres- 
sure of  the  air  in  A  B  =  two  atmospheres.  But  the 
air  has  been  compressed  into  half  the  space  it  for- 
merly occupied,  and  is,  consequently,  twice  as  dense. 
If  the  length  and  strength  of  the  tube  would  admit  of 
a  column  of  mercury  above  the  surface  in  the  short 
arm  equal  to  twice  A  C,  the  air  would  be  compressed 
into  one  third  its  original  bulk  ;  and,  inasmuch  as  it 
would  balance  a  pressure  of  three  atmospheres,  its 
pressure  would  be  increased  threefold. 

This  experiment  may  be  conducted  in  a  more  sci- 
entific manner,  as  follows  :  — 

Experiment  2.  —  Let  the  mercury  be  at  the  same 
level,  A  B  (Fig.  134),  in  both  arms  of  the  tube.     The 
body  of  air  to  be  experimented  with  is  in  the  short  arm  between  A  and 
C.      The   dimensions  of  this  body  can  vary  only  in  hight ;    hence  its 
hight,    H,  may   represent   its  volume.      Measure   II,    i.e.    the   distance 


FIG.  133. 


BOYLE  S    LAW. 


165 


between  A  and  C,  and  regard  the  number  of  inches  (or  centimeters) 
as  representing  the  volume,  V.  Its  pressure,  P,  evidently  is  the  same  as 
that  of  the  atmosphere  at  the  time  of  experimenting. 
Consult  a  barometer,  and  ascertain  the  hight  of  the  baro- 
metric column  ;  let  this  hight  represent  P.  Pour  a  little 
mercury  into  the  tube  ;  the  mercury  rises  to  AI  and  BI. 
Measure  from  AI  to  C  ;  this  number  represents  the  vol- 
ume, Fi,  of  the  body  of  gas  now.  Measure  the  vertical 
distance  between  AI  and  BI  ;  this  number  represents  the 
increase  in  pressure,  which,  added  to  P,  will  give  its 
present  pressure,  PI.  —82 

Now  pour  more  mercury  into  the  long  arm,  so  that  it 
will  rise  to  some  such  points  as  A2  and  B2.  Determine 
as  before  the  new  volume,  F2,  and  new  pressure,  Pg. 
So  continue  to  add  mercury  a  third,  and  a  fourth  time, 
and  get  new  values  for  the  volume,  Fg,  and  Fj,  and 
for  the  pressure,  P3,  and  P4.  Arrange  the  results  as 
follows :  — 


F  = 


etc. 


P  = 
Pi  = 
P2  = 

etc. 


B 


FIG.  134. 


It  will  be  found  that  the  series  of  products  in  the  last 
column  are  approximately  equal  (due  allowance  being  made 
for  errors  in  measurement,  etc.)  ;  consequently  P  varies 
inversely  as  V.  Hence  the  law  :  — 

The  volume  of  a  body  of  gas  at  a  constant  temperature  varies 
inversely  as  its  pressure,  density,  and  elasticity. 

For  many  years  after  the  announcement  of  this  law,  first 
by  Boyle  and  a  little  later  by  Mariotte,  it  was  believed  to 
be  rigorously  correct  for  all  gases ;  but  more  recently,  more 
precise  experiments  have  shown  that  it  is  approximately  but 
not  rigidly  true  for  any  gas,  that  the  departure  from  the  law 
differs  with  different  gases,  and  that  each  gas  possesses  a 
special  law  of  compressibility.  There  is  a  limit  beyond  which 
this  law  does  not  hold.  This  limit  is  soonest  reached  with 
those  gases,  like  carbon-dioxide,  chlorine,  etc.,  that  are  most 


166 


MOLAR    DYNAMICS. 


readily  liquefied  by  pressure.  A  gas  is  nearer  perfect,  or 
conforms  more  nearly  to  Boyle's  law,  in  proportion  as  it  is  at 
a  greater  distance,  as  regards  both  temperature  and  pressure, 
from  its  liquefying  point.  When  a  gas  is  near  the  critical 
state  its  density  increases  more  rapidly  than  its  elasticity.1 

138.  Manometer,  or  pressure  gauge.  —  The  manometer,  an  instru- 
ment for  measuring  the  pressure  of  a  gas  or  vapor  contained  in  a 
closed  vessel,  under  considerable  pressure,  illustrates  the  application 
of  Boyle's  law  to  a  practical  purpose. 

This  instrument  consists,  as  in  Fig.  135,  of  a  bent  tube  A  B  closed 
at  one  end  a,  and  containing  within  the  space 
Art  a  quantity  of  air,  which  is  cut  off  from 
external  communication  by  a  column  of  mer- 
cury. The  apparatus  is  so  constructed  that 
when  the  pressure  on  B  is  equal  to  that  of  an 
atmosphere,  the  mercury  stands  at  the  same 
hight  in  both  branches.  But  if  the  pressure 
increase,  the  mercury  is  forced  into  the  left 
branch,  so  that  the  air  in  that  branch  is  com- 
pressed, and  its  elasticity  proportionately  in- 
creased. The  pressure  of  the  gas  exerted  at  B 
is  then  equal  to  the  pressure  of  the  compressed 
air,  together  with  that  of  a  column  of  mercury 
mn  equal  to  the  difference  of  level  of  the  liquid  in  the  two  branches. 
This  pressure  is  expressed  in  atmospheres  on  the  scale  ab. 

139.  Elasticity  of  gases.  —  The  elasticity  of  all  fluids  is 
perfect.  By  this  is  meant,  that  the  force  exerted 
in  expansion  is,  except  within  certain  limits 
rarely  reached,  equal  to  the  force  used  in  com- 
pression; and  that,  however  much  a  fluid  is 
compressed,  it  will  always  completely  regain 
its  former  bulk  when  the  pressure  is  removed. 
Hence  the  barometer,  which  measures  the  com- 
pressing force  of  the  atmosphere,  also  measures 
at  the  same  time  the  elasticity  of  the  air. 
A  so-called  vacuum  gauge  (Fig.  136)  is  simply  a  short  mer- 

1  The  student  will  find  this  subject  admirably  treated  in  Daniell,  pp.  204,  222,  etc. 


FIG.  135. 


FIG.  136. 


SUCTION. 


167 


cury  barometer,  —  short  because  it  is  seldom  required  to 
make  measurements  except  in  tolerably  high  vacua,  where 
the  mercurial  column  is  correspondingly  low.  For  instance, 
this  apparatus,  placed  under  the  receiver  of  an  air-pump 
from  which  air  is  exhausted,  will  measure  the  elasticity  of 
the  air  in  the  receiver.  This  known,  the  degree  of  exhaustion 
is  readily  determined. 

Experiment  3.  —  Force  the  piston  of  the  seven-in-one  apparatus  two 
thirds  of  the  way  into  the  cylinder,  and  close  the  aper- 
ture. Support  the  apparatus  on  blocks,  with  the  piston 
upwards,  and  place  the  whole  under  the  receiver  of  an 
air-pump.  Exhaust  the  air  from  the  receiver ;  the  outside 
pressure  of  the  air  being  partially  removed,  the  unbalanced 
pressure  of  the  air  enclosed  within  the  cylinder  will  cause 
the  piston  to  rise. 

Experiment  4-  —  Take  a  glass  tube  (Fig.  137)  having  a 
bulb  blown  at  one  end.      Nearly  fill   it  with  water,  so 
that  when  it  is  inverted  there  will  be  only  a  bubble  of  air 
in  the  bulb.     Insert  the  open  end  in  a  glass  of  water,  place  under  a 
receiver,  and  exhaust.     Nearly  all  the  water  will  leave  the  bulb  and  tube. 
Why  ?     What  will  happen  when  air  is  admitted  to  the 
receiver  ? 

140.  Suction.  —  Liquids  are  said  to  be  raised 
by  the  "  force  of  suction,"  which  seems  to  imply 
that  a  lifting  force  acting  from  above  pulls  the 
liquid  up.  Does  this  explain  suction  ? 

Experiment  5.  —  Fill  a  glass  U-tube  having  unequal 
arms  (Fig.  138)  with  water  to  the  level  cb.  Close  the  end 
6  with  a  finger,  and  try  to  suck  the  liquid  out  of  the  tube.  You  find  it 
impossible.  Remove  the  finger  from  6,  and  you  can  suck  the  liquid  out 
with  ease.  Why  ? 


FIG.  137, 


FIG.  138. 


168 


MOLAR    DYNAMICS. 


FJG. 139. 


SECTION  IV. 

INSTRUMENTS    USED    FOR    RAREFYING    AIR. 

141.    The  air-pump. — The  air-pump  is  used  to  rarefy  air 

,  in  a  closed  vessel. 
Fig.  139  will  serve 
to  illustrate  its 
operation.  R  is  a 
p  glass  receiver  within 
which  the  air  is  to 
B  be  rarefied;  B  is  a 
hollow  cylinder  of 
brass,  called  the 
p  u mp  -  barrel  /  the 
plug  P,  called  a  pis- 
ton, is  fitted  to  the 
interior  of  the  bar- 
rel, and  can  be  moved  up  and  down  by  the  handle  H  ;  s  and  t 
are  valves.  A  valve  acts  on  the  principle  of  a  door  intended 
to  open  or  close  a  passage.  If  you  walk  against  a  door  on 
one  side,  it  opens  and  allows  you  to  pass  ;  but  if  you  walk 
against  it  on  the  other  side,  it  closes  the  passage,  and  stops 
your  progress.  Suppose  the  piston  to  be  in  the  act  of 
descending  ;  the  compression  of  the  air  in  B  closes  the  valve 
t,  and  opens  the  valve  s,  and  the  enclosed  air  escapes.  After 
the  piston  reaches  the  bottom  of  the  barrel,  it  begins  its 
ascent.  This  would  cause  a  vacuum  between  the  bottom  of 
the  barrel  and  the  ascending  piston  (since  the  unbalanced 
pressure  of  the  outside  air  immediately  closes  the  valve  s), 
but  the  pressure  of  the  air  in  the  receiver  R  opens  the  valve  t 
and  fills  this  space.  As  the  air  in  R  expands,  it  becomes 
rarefied  and  exerts  less  pressure.  The  external  pressure  of 
the  air  on  R,  being  no  longer  balanced  by  the  pressure  of 


INSTRUMENTS    USED    FOR    RAREFYING    AIR. 


169 


the  air  within,  presses  the  receiver  firmly  upon  the  plate  L. 
Each  repetition  of  a  double  stroke  of  the  piston  removes  a 
portion  of  the  air  remaining  in  R.  The  air  is  removed  from 
R  by  its  own  expansion.  However  far  the  process  of  exhaus- 
tion may  be  carried,  the  receiver  will  always  be  filled  with 
air,  although  it  may  be  exceedingly  rarefied.  The  operation 
of  exhaustion  is  practically  ended  when  the  pressure  of  the 
air  in  R  becomes  too  feeble  to  lift  the  valve  t,  unless  the 
apparatus  be  so  constructed  that  the  valves  are  opened  and 
closed  by  mechanical  action.  It  is  obvious  that  if  s  and  t 
opened  downward  instead  of  upward,  then  as  the  piston  is 
raised  and  depressed,  air  would  be  compressed  in  R.  A  con- 
denser is  merely  a  pump  with  its  valves  reversed,  and  is  used 
to  condense  air. 

142.  The  mercury  air-pump.  —  In  recent  years  the  so-called 
mercury  air-pump  has  largely  displaced  the  pump  described 
above,  since  it  is  capable  of  producing  a  much  greater  rare- 
faction. In  brief,  it  makes  use  of  the  Torricellian  vacuum, 
sueh  as  is  formed  in  the  top  of  a  barometer  tube.  On  account 
of  its  simplicity,  the  Geissler  pump,  the  first  of  the  kind 
invented,  is  chosen  for  illustration.  A  (Fig.  140)  is  a  glass 
tube  more  than  thirty- 
four  inches  long,  having 
a  globe-like  enlargement 
B  of  about  a  Hter  capac- 
ity. Above  this  globe 
leads  a  tube  containing  a 
three-way  stop-cock  and 
a  branch  tube  D.  By 
means  of  this  stop-cock 
B  may  be  placed  in  com- 
munication either  through 
D  with  the  atmosphere, 
as  shown  in  M  (Fig.  141),  or  through  E  with  the  receiver  to 


FIG.  140. 


170  MOLAR   DYNAMICS. 

be  exhausted,  as  shown  in  N.  Connected  with  the  lower  end 
of  A  by  means  of  a  thick  rubber  tube  is  a  vessel  G  containing 
mercury.  The  pump  is  operated  as  follows  :  C  is  turned  as 
in  M,  G  is  raised  so  that  mercury  will  flow  from  it  into  B 
and  fill  it,  the  air  escaping  through  D.  Then  the  stop-cock  is 
placed  as  in  N,  and  G  is  lowered  so  as  to  allow  the  mercury 
to  flow  back  into  it.  A  Torricellian  vacuum  would  be  formed 
in  B  were  it  not  in  communication  through  E  with  the 
receiver.  As  it  is,  the  air  in  this  space  expands  and  fills  B, 
and  is  thus  to  this  extent  rarefied.  By  a  sufficient  number 
of  repetitions  of  this  process,  a  very  high  vacuum  is  obtaina- 
ble. There  are  many  modifications  of  this  pump,  in  some  of 
which  the  stop-cock  is  dispensed  with,  and  consequently  the 
trouble  of  operating  it  is  avoided. 

With  the  common  pump  a  vacuum  of  a  millimeter  of  mer- 
cury is  considered  exceedingly  good ;  but  with  a  mercury  pump 
it  is  easy  to  obtain  a  vacuum  of  .00076  of  a  millimeter,  which 
represents  about  one  millionth  the  normal  pressure  of  the 
atmosphere.  "Rood  in  1881  succeeded  in  obtaining  vacua 
as  high  as  a  three  hundred-millionth  of  an  atmosphere."  — 
Barker. 

SECTION  V. 

SIPHONS    AND    PUMPS    FOB    LIQUIDS. 

143.  Construction  and  operation  of  the  siphon.  —  A  siphon 
is  an  instrument  used  for  transferring  a  liquid  from  one  vessel 
to  another  over  an  elevation  through  the  agency  of  atmo- 
spheric pressure.  It  consists  of  a  tube  of  any  material  (rub- 
ber is  often  most  convenient)  bent  into  a  shape  somewhat 
like  the  letter  U.  To  set  it  in  operation,  fill  the  tube  with 
a  liquid,  stop  each  end  with  a  finger  or  cork,  place  it  in  the 
position  represented  in  Fig.  142,  remove  the  stoppers  and 
the  liquid  will  flow  out  at  the  orifice  o.  Why?  The  up- 


SIPHONS    AND    PUMPS    FOR    LIQUIDS.  171 

ward  pressure  of  the  atmosphere  against  the  liquid  in  the 
tube  is  the  same  at  both  ends ;  hence  these  two  forces  are 
in  equilibrium.  But  the  downward 
pressure  of  the  column  of  liquid  a  b  ° 
is  greater  than  the  downward  pres- 
sure  of  the  column  d  c ;  hence  equi- 
librium is  destroyed  and  the  move- 
ment is  in  the  direction  of  the 
greater  (i.e.  the  unbalanced)  force. 
The  unbalanced  force  which  causes  the  flow  is  equal  to  the 
downward  pressure  of  the  column  e  b. 

If  one  end  of  the  tube  filled  with  liquid  be  immersed  in  a 
liquid  in  some  vessel,  as  in  A  (Fig.  143),  and  the  other  end 
be  brought  below  the  surface  of  the  liquid  in  the  vessel  and 
the  stoppers  be  removed,  the  liquid  in  the  vessel  will  flow  out 
through  the  tube  as  long  as  the  distance  e  b  remains  greater 
than  zero. 


If  one  of  the  vessels  be  raised  a  little,  as  in  C,  the  liquid  will  flow 
from  the  raised  vessel,  till  the  surfaces  in  the  two  vessels  are  on  the 
same  level.  The  remaining  diagrams  in  this  cut  represent  some 
of  the  great  variety  of  uses  to  which  the  siphon  may  be  put.  D,  E, 
and  F  are  different  forms  of  siphon  fountains.  In  D,  the  siphon 
tube  is  filled  by  blowing  in  the  tube  /.  Explain  the  remainder  of 
the  operation.  A  siphon  of  the  form  G  is  always  ready  for  use.  It 
is  only  necessary  to  dip  one  end  into  the  liquid  to  be  transferred. 
Why  does  the  liquid  not  flow  out  of  this  tube  in  its  present  con- 
dition ?  H  illustrates  the  method  by  which  a  heavy  liquid  may  be 
removed  from  beneath  a  lighter  liquid.  By  means  of  a  siphon  a 
liquid  may  be  removed  from  a  vessel  in  a  clear  state,  without 
disturbing  sediment  at  the  bottom.  I  is  a  Tantalus  cup.  A  liquid 
will  not  flow  from  this  cup  till  the  top  of  the  bend  of  the  tube  is 
covered.  It  will  then  continue  to  flow  as  long  as  the  end  of  the 
tube  is  in  the  liquid.  The  siphon  J  may  be  filled  with  a  liquid  that 
is  not  safe  or  pleasant  to  handle,  by  placing  the  end  j  in  the  liquid, 
stopping  the  end  A-,  and  sucking  the  air  out  at  the  end  I  till  the 
lower  end  is  filled  with  the  liquid. 


172  MOLAR    DYNAMICS. 

Gases  heavier  than  air  may  be  siphoned  like  liquids.  Vessel  o 
contains  carbonic  acid  gas.  As  the  gas  is  siphoned  into  the  vessel  p, 
it  extinguishes  a  candle-flame.  Gases  lighter  than  air  are  siphoned 
by  inverting  both  the  vessels  and  the  siphon. 


FIG.  143. 


The  siphon  cannot  elevate  liquids,  it  can  merely  transfer 
liquids  to  places  of  lower  level.  It  is  apparent  that  the 
pressure  of  the  air  drives  the  liquid  through  the  siphon,  and 
that  a  siphon  would  be  inoperative  in  a  vacuum.  Obviously 
the  hight  of  the  bend  to  which  different  liquids  can  be  raised 
varies  with  their  respective  densities.  Thus  the  hight  to 
which  mercury  can  be  raised  is  the  barometric  hight,  while 
water  may  be  raised  13.6  times  as  high. 


SIPHONS    AND    PUMPS    FOR    LIQUIDS. 


173 


144.  Lifting  or  suction  pump.  - —  The  common  lifting-pump 
is  constructed  like  the  barrel  of  an  air-pump.  Fig.  144  rep- 
resents the  piston  B  in  the  act  of  rising.  As  the  air  is  rarefied 
below  it,  water  rises  in  consequence  of  atmospheric  pressure 
on  the  water  in  the  well,  and  opens  the  lower  valve  D. 


FIG.  145. 


FIG.  146. 


FIG.  144. 


Atmospheric  pressure  closes  the  upper 
valve  C  in  the  piston.  When  the  piston  is 
pressed  down  (Fig.  145),  the  lower  valve 
closes,  the  upper  valve  opens,  and  the 
water  between  the  bottom  of  the  barrel 
and  the  piston  passes  through  the  upper 
valve  above  the  piston.  When  the  piston  is  raised  again 
(Fig.  146),  the  water  above  the  piston  is  raised  and  discharged 
from  the  spout. 

The  liquid  is  sometimes  said  to  be  raised  in  a  lifting-pump 
by  the  "force  of  suction."  Is  there  such  a  force? 

Calling  the  specific  density  of  mercury  13.6  and  disregarding 
the  vapor  pressure  of  mercury  (.02mm  at  20°  C.),  a  water 
barometer  would  be  76  X  13.6  =  1033.6  cm  high  when  the 
mercury  barometer  stands  at  76  cm,  provided  there  were  no 
pressure  exerted  by  the  vapor  of  water.  But  at  20°  C.  the 


174 


MOLAR    DYNAMICS. 


pressure  of  water  vapor  is  1.74cm  of  mercury  =  1.74  X  13.  G 
(=  23.7  cm)  centimeters  of  water.  Therefore  the  hight  of  the 
water  barometer  would  be  1033.6  —  23.7  =  1009.9  cm,  and  this 
is  the  limit  of  the  hight  to  which  water  can  be  raised  by  the 
pressure  of  air  in  a  suction  pump  under  these  conditions.1 

145.  Suction  and  force-pump  combined.  —  In  this  pump  the 
ordinary  piston  with  valve  and  leather  washers  is  replaced 
by  a  solid  cylinder  of  metal,  B  (Fig.  147),  called  the  plunger. 

This  passes  through  a  stuffing  box 
D,  in  which  it  fits  air-tight.  Valves 
opening  upward  and  outward  are 
placed  at  A  and  C  respectively. 
When  the  plunger  is  raised,  A 
opens  and  C  closes,  and  water  is 
raised  into  the  barrel  by  atmos- 
pheric pressure.  When  the  plunger 
descends,  A  closes  and  C  opens,  and 
the  water  is  forced  up  through  the 
pipe  E  to  a  hight  dependent  on  the 
pressure  brought  to  bear  upon  it 
through  the  plunger.  An  air-dome 
F  is  usually  connected  with  these 
pumps  to  regulate  the  pressure  so 
as  to  give  through  the  delivery  pipe  a  very  steady  stream. 
This  dome  contains  air.  When  the  plunger  descends  it  forces 
water  violently  into  E  and  thus  tends  to  produce  a  severe 
strain  in  the  pipe.  But  the  water  enters  the  dome,  compresses 
the  elastic  air  within,  and  thus  the  shock  is  largely  reduced. 
As  soon  as  the  down  stroke  of  the  piston  ceases,  the  valve  C 
closes,  and  the  compressed  air  in  the  dome  forces  the  water 
out  through  E  in  a  continuous  stream. 


FIG.  147. 


1  At  50°  the  limit  would  be  1033.6  -  (9.2  x  13.6)  =  908.4  cm.  At  100°  the  hight  would 
be  1033.6  —  (76  x  13.6)  =  0  cm,  the  pressure  of  water  vapor  being  equal  to  the  pressure 
of  the  atmosphere. 


BUOYANCY    OF   FLUIDS.  175 

SECTION  VI. 

BUOYANCY    OF    FLUIDS. 

146.  Why  a  solid  is  buoyed  up  by  a  fluid,  and  with  how 
great  a  force  it  is  buoyed  up.  —  Suppose  deb  a  (Fig.  148)  to 
be  a  cubical  block  of  marble  immersed  in  a  liquid.  It  is 
obvious  that  the  downward  pressure  upon  the  surface  da  is 
equal  to  the  weight  of  the  column  of  liquid 
edao.  The  upward  pressure  on  the  surface 
cb  is  equal  to  the  weight  of  a  column  of 
liquid  ecbo.  The  difference  between  the 
upward  pressure  against  cb  and  the  down- 
ward pressure  on  da,  is  the  weight  of  a 
column  of  liquid  ecbo  less  the  weight  of  a 
column  of  liquid  edao,  which  is  a  column  of 


liquid  deb  a   (ecbo  —  edao  =  dcba).     But          FlG  148 
a  column  of  liquid  deb  a  has  precisely  the 
volume  of  the  solid  submerged.     Therefore,  a  solid  is  buoyed 
up  by  a  fluid  in  consequence  of  the  unequal  pressures  upon  its 
top  and  bottom  at  their  different  depths,  and  the  amount  of  the 
buoyancy  is  the  weight  of  a  volume  of  that  fluid  equal  to  the 
volume  of  the  immersed  solid. 

This  principle  1  may  be  thus  stated :  a  solid  immersed  in  a 
fluid  is  buoyed  up  by  a  force  equal  to  the  weight  of  the  fluid 
displaced.  The  difference  between  the  weight  of  a  body  and 
the  buoyant  force  of  a  fluid  in  which  it  is  submerged  may  be 
called  the  effective  weight  of  the  body  in  that  fluid. 

Experiment  1.  —  Suspend  from  one  arm  of  a  balance  beam  a  cylin- 
drical bucket  A  (Fig.  149),  and  from  the  bucket  a  solid  cylinder  whose 
volume  is  exactly  equal  to  the  capacity  of  the  bucket ;  in  other  words,  the 
latter  would  just  fill  the  former,  Counterpoise  the  bucket  and  cylinder 
with  weights. 

1  This  principle  is  commonly  called  the  Archimedes  principle  from  the  name  of 
the  discoverer  (287  to  212  B.C.). 


176 


MOLAR    DYNAMICS. 


FIG.  149. 


Place  beneath  the  cylinder  a  tumbler  of  water,  and  raise  the  tumbler 
until  the  cylinder  is  completely  submerged.     The  buoyant  force  of  the 
water  destroys  the  equilibrium.    Pour  water 
into  the  bucket ;  when  it  becomes  just  even 
full,  the  equilibrium  is  restored. 

Now  it  is  evident  that  the  cylinder 
immersed  in  the  water  displaces  its  own 
volume  of  water,  or  just  as  much  water 
as  fills  the  bucket.  But  the  bucket  full  of 
water  is  just  sufficient  to  restore  the  weight 
lost  by  the  submersion  of  the  cylinder. 
What  principle  does  this  experiment  illus- 
trate ? 

A  floating  body,  as  a  cork  on  water, 
has  no  effective  weight.  It  sinks 
until  it  displaces  a  weight  of  the  fluid 
equal  to  its  own  weight,  or  until  it 

reaches  a  depth  where  the  upward  pressure  of  the  fluid  is  equal 

to  its  own  weight. 

Experiment  2.  — Place  a  baroscope  (Fig.  150),  consisting  of  a  scale- 
beam,  a  small  weight,  and  a  hollow  brass  sphere,  under  the  receiver  of  an 
air-pump,  and  exhaust  the  air.  In  the  air  the  weight  and  sphere  balance 
each  other;  but  when  the  air  is  removed,  the 
sphere  sinks,  showing  that  in  reality  it  is  heavier 
than  the  weight.  In  the  air  each  is  buoyed  up  by 
the  weight  of  the  air  it  displaces;  but  as  the 
sphere  displaces  more  air,  it  is  buoyed  up  more. 
Consequently,  when  the  buoyant  force  is  with- 
drawn from  both,  their  equilibrium  is  destroyed. 

Ordinary  weighing  conducted  in  the  air 
consists,  therefore,  in  a  comparison  of 
effective  weights  in  that  fluid.  The  abso- 
lute weight  is,  evidently,  the  effective 
weight  plus  the  weight  of  the  excess  of  air 
displaced  by  the  body  over  that  displaced  by  the  weights,  or 
it  is  the  weight  of  the  body  in  a  vacuum. 


DENSITY    AND    SPECIFIC    DENSITY.  177 

The  density  of  the  atmosphere  is  greatest  at  the  surface  of 
the  earth.  A  body  free  to  move  cannot  displace  more  than 
its  own  weight  of  a  fluid ;  therefore  a  balloon,  which  is  a 
large  bag  filled  with  a  gas  about  fourteen  times  lighter  than 
air  at  the  sea-level,  will  rise  till  the  weight  of  the  balloon, 
together  with  its  car  and  cargo,  equals  the  weight  of  the  air 
displaced. 

SECTION  VII. 

DENSITY    AND    SPECIFIC    DENSITY. 

147.  Meaning  of  the  terms  and  their  relation  to  each  other. 
—The  density  of  a  substance  at  any  temperature  is  the  mass  of 
a  unit  volume  of  the  substance  at  that  temperature.  Thus,  the 
density  of  water  at  4°  C.  is  one  gram  per  cubic  centimeter,  and 
the  density  of  cast  iron  at  the  same  temperature  is  about  7.12 
grams  per  cubic  centimeter.  The  mean  density  of  a  body  is 
found  by  dividing  its  mass  by  its  volume.  Thus  if  the  mass 
of  a  body  be  30  grams  and  its  volume  be  6  cubic  centimeters, 
its  mean  density  is  (30  -i-  6  — )  5  grams  per  cubic  centimeter. 

The  dimensional  equation  for  density  (D)  is  [D]  =  rTT8  =  [M]  [L]~3. 

As  every  substance  has  a  special  density  of  its  own,  the 
special  (specific)  density  of  any  substance  is  most  conveniently 
measured  by  comparison  with  the  density  of  some  substance 
chosen  as  a  standard. 

The  specific  density  of  a  substance  at  any  temperature  is  the 
ratio  of  its  density  at  that  temperature  to  the  density  of  some 
standard,  i.e.  it  is  the  ratio  between  the  masses  of  equal  volumes 
of  a  given  substance  and  of  some  standard  substance;  or,  since 
weight  at  the  same  place  is  proportional  to  mass,  it  is  the 
ratio  between  the  weights  of  equal  volumes  of  the  substance  and 
of  the  standard.  The  latter  ratio  is  commonly  known  as  the 
specific  gravity  of  the  substance. 


178  MOLAR   DYNAMICS. 

It  must  be  carefully  borne  in  mind  that  density  represents 
a  definite  number  of  units  of  mass  (i.e.  the  number  contained 
in  some  unit  of  volume)  and  is  therefore  a  concrete  number ; 
while  specific  density  is  simply  a  ratio,  and  hence  an  abstract 
number. 

The  standard  adopted  in  scientific  work  for  solids  and 
liquids  is  the  density  of  distilled  water  at  4°  C.  In  the  metric 
system  the  number  which  expresses  the  numerical  value  of 
the  density  of  a  substance  and  the  number  which  expresses 
the  specific  density  of  the  substance  are  identical ;  the  latter, 
being  a  ratio,  is,  of  course,  an  abstract  number.  Thus  the 
density  of  water  being  one  gram  per  cubic  centimeter  at  4°  C., 
and  the  density  of  cast  iron  at  the  same  temperature  being 
7.12  grams  per  cubic  centimeter,  the  ratio  of  the  latter  to 
the  density  of  the  former  (i.e.  the  specific  density  of  iron) 
is  7.12,  which  is  the  same  as  the  numeric  of  the  density  of 
iron. 

148.  Formulas  for  specific  density.  —  Let  D  represent  the 
density  of  any  given  substance,  and  D'  the  density  of  water, 
and  let  W  and  W  represent  respectively  the  weights  of  equal 
volumes  of  the  same  substances  ;  then,  by  definition, 

x  Density  of  given  substance      D 
£>-       Density  of  water  =  5;=  SP"  D- OT 

„>    Weight  of  a  given  volume  of  the  substance W._«      j^ 

Weight  of  equal  volume  of  water  W 

149.  Experimental  methods  of  finding  the  specific  densities 
of  substances.  —  (1)  Solids.  —  The  Principle  of  Archimedes  is 
commonly  applied  to  determine  the  specific  densities  of  solids. 

Experiment  1.  — From  a  hook  beneath  a  scale-pan  (Fig.  151)  suspend 
by  a  fine  thread  a  small  portion  of  the  solid  substance  whose  specific 
density  is  to  be  found,  and  weigh  it,  while  dry,  in  the  air.  Then  immerse 
the  body  in  a  tumbler  of  water  (see  that  it  is  completely  submerged),  and 
weigh  it  in  water.  The  loss  of  weight  in  water  is  evidently  W,  i.e.  the 


DENSITY    AND    SPECIFIC    DENSITY. 


179 


weight  of  the  water  displaced  by  the  body ;  or,  in  other  words,  the  weight 
of  a  body  of  water  having  the  same  volume  as  that  of  the  specimen. 
Apply  the  formula  (2)  for  finding  the  specific 
density. 

Experiment  2.  —  Take  a  piece  of  sheet  lead 
one  inch  long  and  one-half  inch  wide,  weigh 
it  in  air  and  then  in  water,  and  find  its  loss 
of  weight  in  water.  Weigh  in  air  a  piece  of 
cork  or  other  substance  that  floats  in  water ; 
then  fold  the  lead-sinker,  place  it  astride  the 
string  just  above  the  specimen,  completely 
immerse  both,  and  find  their  combined  weight 
in  water.  Subtract  their  combined  weight  in 
water  from  the  sum  of  their  weights  in  air ; 
this  gives  the  weight  of  water  displaced  by  both, 
weight  lost  by  the  lead  alone,  and  the  remainder  is  W,  i.e.  the  weight 
of  water  displaced  by  the  cork.  Apply  formula  (2),  as  before. 

Prepare  blanks,  and  tabulate  the  results  of  the  experiments  as  follows  : 


FIG.  151. 
Subtract  from  this  the 


NAME  OF  SUBSTANCE. 

W  in 
Grams. 

Win 
Grams. 

Sp.  D. 

E. 

Lead     

7  2 

0  66 

10  9 

0  4 

When  the  result  obtained  differs  from  that  given  in  the  table  of 
specific  densities  (Appendix),  the  differ- 
ence is  recorded  in  the  column  of  errors 
(E).  The  results  recorded  in  the  column 
of  errors  are  not  necessarily  real  errors  ; 
they  may  indicate  the  degree  of  impurity, 
or  some  peculiar  physical  condition  of  the 
specimen  tested. 

(2)  Liquids. 

Experiment  3.  —  Take  a  bottle   that 
holds  when  filled  a  certain  (whole)  num- 
FIG.  152.  ber  of  grams  of  water,  e.g.  100  g,  200  g, 


180 


MOLAR  DYNAMICS. 


etc.  Fill  the  bottle  with  the  liquid  whose  specific  density  is  sought. 
Place  it  on  a  scale-pan  (Fig.  152),  and  on  the  other  scale-pan  place  a  piece 
of  metal  a  which  is  an  exact  counterpoise  for  the  bottle  when  empty. 
On  the  same  pan  place  weights  6,  until  there  is  an  equilibrium.  The 
weights  placed  in  this  pan  represent  the  weight  W  of  the  liquid  in  the 
bottle.  Apply  formula  (2).  The  W  (i.e.  the  100 g,  200 g,  etc.)  is  usually 
etched  on  bottles  constructed  for  this  purpose. 

Experiment  4- — Take  a  pebble  stone  (e.g.  quartz)  about  the  size  of  a 
large  chestnut ;  find  its  loss  of  weight  (i.  e.  W')  in  water ;  find  its  loss  of 
weight  (i.e.  W)  in  the  given  liquid.  Apply  formula  (2). 

Experiment  5.  —  Insert  the  glass  tube  B  (Fig.  153)  into  a  tumbler  of 
the  liquid  whose  specific  density  is  sought,  and  tube  C  into  a  tumbler 
of  water.  Attach  a  stop-cock  to  the  rubber  connector  D, 
raise  the  liquids  a  little  way  in  their  respec- 
tive tubes  by  suction,  close  the  stop-cock,  and 
measure  the  hights  (m  and  n  respectively)  of  the 
columns  in  B  and  C  above  the  surfaces  of  the 


Then  -  =  the 
m 


liquids  in   the  tumblers  below. 
n  specific  density  of  the  liquid  in  B. 

150.  The  densimeter.  —  The  principle 
of  the  densimeter  (commonly  but  inappro- 
priately called  the  hydrometer']  is  based 
upon  two  facts  :  (1)  a  floating  solid  sinks 
until  it  displaces  its  own  weight  of  the 
liquid  in  which  it  floats  ;  (2)  the  volumes 
of  two  liquids  displaced  by  the  same  float- 
ing solid  vary  inversely  as  their  densities. 


FIG  153  Experiment  6. — Take  a  prism  of  paraffined 

wood  (Fig.  154)  i  inch  square  and  5  inches  long, 

with  a  quarter-inch  scale  on  one  of  its  faces.  It  should  be  so  loaded  as 
to  assume  a  vertical  position  and  sink  just  4  inches  when  placed  in  water. 
It  displaces  therefore  a  volume,  V,  (£  x  £  x  4  =  1  cu.  in.)  of  water. 

Place  it  in  some  liquid  whose  specific  density  is  sought.     It  displaces  a 

y 
volume,  V',  of  this  liquid.     Then  —  =  the  specific  density  of  the  given 

liquid.  This  experiment  illustrates  the  principle  on  which  the  densimeter 
is  based. 


MISCELLANEOUS    EXPERIMENTS. 


181 


FIG.  155. 


Instead  of  a  prism  of  wood,  a  glass  tube  A  (Fig.  155)  terminating  in  a 
bulb  containing  shot  or  mercury  is  generally  used.  It  has  a  scale  of 
specific  densities  on  the  stem,  so  that  no  computation  is  necessary.  The 
experimenter  merely  places  it  in  the  liquid  to  be 
tested,  and  reads  the  specific  density  at  that  point,  B, 
which  is  at  the  surface  of  the  liquid. 

(3)    Gases. 

The  specific  density  of  a  gas  is  found  by  the 
application  of  the  same  principles  as  those  em- 
ployed in  determining  that  of  a  liquid,  but  the 
operation  is  attended  with  peculiar  difficulties. 
Air  is  extracted  from  a  light  capacious  glass  or 
copper  globe  by  means  of  a  good  air-pump,  and 
the  empty  vessel  is  weighed.  It  is  then  put  in 
communication,  by  means  of  a  stop-cock,  with 
a  reservoir  containing  the  gas  to  be  tested,  which 
must  be  perfectly  pure  and  dry.  Gas  is  allowed 
to  enter  the  globe  slowly  until  the  pressure  is 
the  same  as  the  atmospheric  pressure  outside,  and  then  it  is  allowed 
to  stand  until  the  gas  acquires  the  temperature  of  the  air  outside. 
The  vessel  thus  filled  with  gas  is  again  weighed  ;  its  gain  in  weight  is 
the  weight  of  the  gas  (W)  which  fills  the  globe.  The  globe  is  again 
exhausted  and  filled,  at  the  same  temperature  and  pressure,  with 
a  gas  which  is  employed  as  a  standard.  The  weight  of  the  gas  now 
filling  the  globe  is  found.  Then  the  weight  of  the  given  gas  divided 
by  the  weight  of  an  equal  volume  of  the  standard  gas  at  the  same 
temperature  and  pressure  is  the  specific  density  of  the  given  gas. 

For  many  purposes  it  is  most  convenient  to  employ  hydrogen 
gas  —  the  lightest  gas  —  as  a  standard  for  gases.  Then  assuming 
the  density  of  hydrogen  to  be  1,  that  of  air  is  14.47,  oxygen  16,  etc. 
A  cubic  centimeter  of  hydrogen  at  0°  C.  and  at  the  barometric 
pressure  of  760mm  weighs  at  Paris  0. 0000895682  g,  and  a  cubic 
centimeter  of  dry  pure  air  under  the  same  conditions  weighs 
0.0012032  g. 

151.    Miscellaneous  experiments. 

Experiment  7.  —  Find  the  volume  of  an  irregular  shaped  body,  e.g. 
a  stone.  Find  its  loss  of  weight  in  water.  Remember  that  the  loss  of 
weight  is  precisely  the  weight  of  the  water  it  displaces,  and  that  the 
volume  of  one  gram  of  water  is  one  cubic  centimeter. 


182  MOLAR    DYNAMICS. 

Experiment  8.  —  Find  the  capacity  of  a  test-tube,  or  of  an  irregular 
shaped  cavity  in  any  body.  Weigh  the  body ;  then  fill  the  cavity  with 
water,  and  weigh  again.  As  many  grams  as  its  weight  is  increased,  so 
many  cubic  centimeters  is  the  capacity  of  the  cavity. 

Experiment  9.  —  A  fresh  egg  sinks  in  water.  See  if  by  dissolving 
table  salt  in  the  water  it  can  be  made  to  float.  How  does  salt  affect  the 
density  of  the  water  ? 

Experiment  10.  —  Float  a  sensitive  densimeter  in  water  at  about 
60° F.  (15°  C.),  and  in  other  water  at  about  180° F.  (82°  C.).  Which  water 
is  denser? 

Exercises. 

•  1.  Can  you  by  placing  the  neck  of  a  bottle  in  your  mouth  suck  liquid 
out  of  the  bottle  ?  Explain.  ^/  A 

» 2.  a.  What  is  the  weight  of  a  liter  of  hydrogen  under  a  pressure  of 
760  mm  and  at  0°  C.  ?'  6.  What  is  the  weight  of  a  liter  of  dry  air  under 
the  same  conditions  ?  / '  i  ?  S  ^  $* 

-  3.  Suppose  that  when  the  barometer  stands  at  76  cm,  the  pressure  of 
air  within  the  seven-in-one  apparatus  (Fig.  105)  is  diminished  one-fourth. 
The  diameter  of  the  piston  being  5.75  inches,  what  pulling  force  must  be 
employed  to  prevent  the  piston  from  being  forced  in,  on  the  supposition 
that  there  is  no  friction  ? 

» 4.  Into  what  space  must  you  compress  30  cu.  ft.  of  air  that  its  elastic 
force  may  be  made  five  times  as  great  ?  4  C/OC  I 

5.  If  when  the  barometer  stands  at  760  mm  a  cubic  meter  of  air  be 
forced  into  a  vessel  whose  capacity  is  1000  cc,  what  pressure  will  be 
exerted  upon  its  interior  walls  ? 

6.  How  high  can  naphtha  be  raised  by  a  lifting  pump  ? 
.7.    Why  do  iron-clad  vessels  float  in  water  ? 

8.  A  block  of  ice  weighing  500  grams  floats  on  water,  a.  What  vol- 
ume of  water  does  it  displace  ?  6.  What  volume  of  ice  is  out  of  water  ? 

•9.    Will  ice  float  or  sink  in  alcohol  ?  ^v^Jk. 

*10.  Give  the  density  and  specific  density  of  gold,  cork,  and  alcohol. 

*11.  The  effective  weight  of  a  stone  in  water  is  56  grams  ;  its  weight  in 
air  is  112  grams,  a.  What  is  the  volume  of  the  stone  ?  ,  b.  What  is  its 
density?  -  » 

12.  How  many  cubic  centimeters  of  dry  air  at  760  mm  and  0°  C.  weigh 
as  much  as  one  cubic  centimeter  of  water  at  4°  C.  ? 

•13.  If  4  cubic  feet  of  a  body  have  a  mass  of  180  Ibs.,  what  is  its  specific 
density  ?  y  5 


EXERCISES. 


183 


08 


14.    How  much  will  1  K  of  copper  weigh  in  water  ? 

*  15.    What  does  a  piece  of  lead  20  x  10  X  5  cm  weigh  ?  | 
*16.    What  would  it  weigh  in  water  ?        /  (    b  (A  « 

17.    What  would  it  weigh  in  mercury  ?  ,  Q 

*  18.    How  much  does  a  cubic  foot  of  gold  weigh?     )  /  0  /  J»»  I 

,  19.  A  solid  body  weighs  10  pounds  in  air  and  6  pounds  in  water,  a. 
What  is  the  weight  of  an  equal  volume  of  water  ?  b.  What  is  its  specific 
density  ?  c.  What  is  the  volume  of  the  body  ?  d.  What  would  it  weigh 
if  it  were  immersed  in  sulphuric  acid  ? 

•"•UO.  A  thousand-gram  bottle  filled  with  sea-water  requires  in  addition 
to  the  counterpoise  of  the  bottle  1026  grams  to  balance  it.  a.  What  is 
the  specific  density  of  sea-  water  ?  6.  What  is  the  quantity  of  salt,  etc.  , 
dissolved  in  1000  grams  of  sea-water  ? 

-21.  A  piece  of  cork  floating  on  water  displaces  2  pounds  of  water. 
What  is  the  weight  of  the  cork  ? 

*22.    In  which  would  a  hydrometer  sink  farther,  in  milk  or  in  water? 

*  23.    What  metals  will  float  in  mercury  ? 

•24.  a.  Which  has  the  greater  specific  density,  water  at  10°  C.  or  water 
at  20°  C.  ?  6.  If  water  at  the  bottom  of  a  vessel  could  be  raised  by 
application  of  heat  to  20°  C.  while  the  water  near  the  upper  surface  had 
a  temperature  of  10°  C.  ,  what  would  happen  ? 

*  25.    A  block  of  wood  weighs  550  grams  ;   when  a  certain  irregular- 
shaped  cavity  is  filled  with  mercury  the  b'lock  weighs  570  grams.     What 
is  the.  capacity  of  the  cavity  ? 

v  26.  In  which  is  it  easier  for  a  person  to  float,  in  fresh  water  or  in  sea- 
water  ?  Why  ? 

1  27.  Fig.  156  represents  a  beaker  graduated  in 
cubic  centimeters.  Suppose  that  when  water  stands 
in  the  graduate  at  50  cc,  a  pebble  stone  is  dropped 
into  the  water,  and  the  water  rises  to  75  cc.  a. 
What  is  the  volume  of  the  stone  ?  6.  How  much 
less  does  the  stone  weigh  in  water  than  in  air  ?  c. 
What  is  the  weight  of  an  equal  volume  of  water  ? 

^  28.  If  a  piece  of  cork  be  floated  on  water  in  a 
graduate,  and  displace  (i.e.  cause  the  water  to  rise) 
7  cc,  what  is  the  weight  of  the  cork  ?  , 

N  29.  You  wish  to  measure  out  50  g  of  sulphuric 
acid.  To  what  number  on  a  beaker  graduated  in 
cubic  centimeters  will  that  correspond  ?  1  "7 

•>  30.  State  how  you  would  measure  out  80  g  of  nitric  acid  in  a  meas- 
uring-beaker. ^  *V  l~> 


FlG  15g 


184  MOLAR    DYNAMICS. 

31.  A  measuring-beaker  contains  35  cc  of  naphtha.      What  is  the 
weight  of  the  naphtha  ? 

32.  If  15  g  of  salt  be  dissolved  in  1  liter  of  water  without  increasing  the 
volume  of  the  liquid,  what  will  be  the  specific  density  of  the  solution  ? 

33.  A  mass  of  lead  weighs  1   K  in  air.      What  will  it  weigh  in  a 
vacuum  ? 

>  34.  A  mass  whose  weight  in  air  is  30  g,  weighs  in  water  26  g,  and 
in  another  liquid  27  g.  What  is  the  specific  density  of  the  other 
liquid  ?  i'jf 

35.  A  silver  spoon  weighing  150  g  is  supported  by  a  string  in  water. 
What  part  of  the  weight  is  sustained  by  the  string,  and  what  part  is  sup- 
ported by  the  wrater  ? 

-<36.    Find  the  specific  density  of  wax  from  the  following  data :  weight 
of  a  given  mass  of  wax  in  air  is  80  g  ;  wax  and  sinker  displace  102.88  cc 
of  water ;  sinker  alone  displaces  14  ccv^l/  ^/ 
•^37.    A  boat  displaces  25  in3  of  water.     How  much  does  it  weigh  ? 

•<  38.  If  50  K  of  stone  were  placed  in  the  boat,  how  much  water  would 
it  displace  ? 

39.  If  the  boat  be  capable  of  displacing  100  m3  of  water,  what  weight 
must  be  placed  in  it  to  sink  it  ? 

40.  An  empty  glass  globe  weighs  100  g  ;  full  of  air  it  weighs  102.4  g  ; 
full  of  chlorine  gas,  it  weighs  105.928  g.     What  is  the  specific  density  of 
chlorine  gas  ? 

41.  What  mass  of  alcohol  can  be  put  into  a  vessel  whose  capacity  is 
1  liter? 

42.  A  solid  floats  at  a  certain  depth  in  a  liquid  when  the  vessel  which 
contains  it  is  in  the  air ;  if  the  vessel  be  placed  in  a  vacuum,  will  the 
solid  sink,  rise,  or  remain  stationary,? 

"*  43.  When  the  volume  of  a  body  of  gas  diminishes,  is  it  due  to  con- 
traction or  compression,  i.e.  to  internal  or  external  forces? 

44.  What  is  the  hight  of  the  barometer  column  when  the  atmospheric 
pressure  is  10  grams  per  square  centimeter  ? 

~  45.  A  barometer  in  a  diving-bell  stands  at  196  cm  when  a  barometer 
at  sea-level  stands  at  76  cm ;  what  is  the  depth  of  the  surface  of  water 
inside  the  bell,  below  the  air-exposed  surface  of  the  water  above  ? 

46.  A  measuring  glass  graduated  in  cubic  centimeters  contains  water. 
An  empty  bottle  floats  on  the  water,  and  the  surface  of  the  water  stands 
at  50  cc.     If  10  g  of  lead  shot  be  placed  in  the  bottle,  where  will  the 
surface  of  the  water  stand  ? 

47.  A  person  can  lift  just  200  K  of  copper  in  water ;  howsinuch  can 
he  lift  in  the  air  ? 


EXERCISES.  185 

48.    If  a  liter  of  gas  under  a  pressure  of  76  mm  be  allowed  to  expand 

and  fill  a  vessel  having  a  capacity  of  10  liters,  what  pressure  will  it 

exert  ? 
-^.49.    A  piece  of  lead  and  a  piece  of  cork  balance  each  other  in  the  air. 

Which  contains  more  matter,  and  how  much  more  ? 
_^«.  50.   How  great  a  buoyant  force  does  a  fluid  exert  on  a  body  immersed 

in  it? 


186  MOLAR   DYNAMICS. 


CHAPTER  V. 

ENERGY  OF  MASS  VIBRATION.  —  SOUND-WAVES. 
SECTION  I. 

ORIGIN    OF   SOUND-WAVES  ;     TRANSMISSION   OF   SOUND-WAVES. 

152.  How  sound  originates.  —  Listen  to  a  sounding  church 
bell.  It  produces  a  sensation ;  it  is  heard.  The  ear  is  the 
organ  through  which  the  sensation  of  hearing  is  produced. 
The  bell  is  at  such  a  distance  that  it  cannot  act  directly  on 
the  ear ;  yet  something  must  act  on  the  ear,  and  it  must  be 
the  bell  which  causes  that  something  to  act. 

How  does  a  sounding  body  differ  from  a  silent  body  ? 

Experiment  1.  —  Strike  a  bell  or  a  glass  bell-jar,  and  touch  the  edge 
with  a  small  ivory  ball  suspended  by  a  thread ;  you  not  only  hear  the 
sound,  but,  at  the  same  time,  you  see  a  tremulous  motion  of  the  ball, 
caused  by  a  motion  of  the  bell.  Touch  the  bell  gently  with  a  finger,  and 
you  feel  a  tremulous  motion.  Press  the  hand  against  the  bell ;  you  stop 
its  vibratory  motion,  and  at  that  instant  the  sound  ceases.  Strike  the 
prongs  of  a  tuning-fork,  and  press  the  stem  against  a  table ;  you  hear  a 
sound.  Thrust  the  ends  of  the  prongs  just  beneath  the  surface  of  water ; 
the  water  is  thrown  off  in  a  fine  spray  on  either  side  of  the  vibrating  fork. 
Watch  the  strings  of  a  piano,  guitar,  or  violin,  or  the  tongue  of  a  Jews- 
harp,  when  sounding.  You  can  see  that  they  are  in  motion. 

Sound  originates  in  mass-vibration. 

How  can  a  bell  sounding  at  a  distance  affect  the  ear?  If 
the  bell  while  sounding  possess  no  peculiar  property  except 
motion,  then  it  has  nothing  to  communicate  to  the  ear  but 
motion.  But  motion  can  be  communicated  by  one  body  to 
another  at  a  distance  only  through  some  medium. 


HOW    SOUND    ORIGINATES.  187 

Experiment  2.  —  Lay  a  thick  tuft  of  cotton-wool  on  the  plate  of  an 
air-pump,  and  on  this,  face  downward,  place  a  loud-ticking  watch,  and 
cover  with  the  receiver.  Notice  that  the  receiver,  interposed  between 
the  watch  and  your  ear,  greatly  diminishes  the  sound,  or  interferes  with 
the  passage  of  something  to  the  ear.  Take  a  few  strokes  of  the  pump 
and  listen  ;  the  sound  is  more  feeble,  and  continues  to  grow  less  and  less 
distinct  as  the  exhaustion  progresses,  until  either  no  sound  can  be  heard 
when  the  ear  is  placed  close  to  the  receiver,  or  an  extremely  faint  one, 
as  if  coming  from  a  great  distance.  The  removal  of  air  from  a  portion  of 
the  space  between  the  watch  and  your  ear  destroys  the  sound.  Let  in 
the  air  again,  and  the  sound  is  restored. 

The  vibrations  of  a  sonorous  body  cannot  affect  the  organ  of 
hearing  without  a  continuous  medium  of  communication  between 
them. 

153.  How  vibratory  motion,  i.e.  a  wave,  is  propagated  through 
an  elastic  medium. 

Experiment  3.  — Fig.  157  represents  a  brass  wire  wound  irito  the  form 
of  a  spiral  spring,  about  12  feet  long.  Attach  one  end  to  a  cigar-box, 
and  fasten  the  box  to  a  table.  Hold  the  other  end  of  the  spiral  firmly  in 
one  hand,  and  with  the  other  hand  insert  a  knife-blade  between  the  turns 
of  the  wire,  and  quickly  rake  it  for  a  short  distance  along  the  spiral 
toward  the  box,  thereby  crowding  closer  together  for  a  little  distance  (B) 


FIG.  157. 

the  turns  of  wire  in  front  of  the  hand,  and  leaving  the  turns  behind 
pulled  wider  apart  (A)  for  about  an  equal  distance.  The  crowded  part 
of  the  spiral  may  be  called  a  condensation,  and  the  stretched  part  a  rare- 
faction. The  condensation,  followed  by  the  rarefaction,  runs  with  great 
velocity  through  the  spiral,  strikes  the  box,  producing  a  sharp  thump ;  is 
reflected  from  the  box  to  the  hand,  and  from  the  hand  again  to  the  box, 
producing  a  second  thump  ;  and  by  skillful  manipulation  three  or  four 
thumps  will  be  produced  in  rapid  succession.  If  a  piece  of  twine  be  tied 
to  some  turn  of  the  wire,  it  will  be  seen,  as  each  wave  passes  it,  to  receive 
a  slight  jerking  movement  forward  and  backward  in  the  direction  of  the 
length  of  the  spiral. 


188  MOLAR    DYNAMICS. 

How  is  energy  transmitted  through  the  spring  so  as  to 
deliver  the  blow  on  the  box?  Certainly  not  by  a  bodily 
movement  of  the  spiral  as  a  whole,  as  might  be  the  case  if  it 
were  a  rigid  rod.  The  movement  of  the  twine  shows  that  the 
only  motion  which  the  coil  undergoes  is  a  vibratory  movement 
of  its  turns.  Here,  as  in  the  case  of  water-waves,  energy 
is  transmitted  through  a  medium  by  the  transmission  of 
vibrations. 

The  effect  of  applying  force  with  the  hand  to  the  spiral 
spring  is  to  produce  in  a  certain  section,  B,  of  the  spiral  a 
crowding  together  of  the  turns  of  wire,  and  at  A  a  separation ; 
but  the  elasticity  of  the  spiral  instantly  causes  B  to  expand, 
the  effect  of  which  is  to  produce  a  crowding  together  of  the 
turns  of  wire  in  front  of  it,  in  the  section  C,  and  thus  a  for- 
ward movement  of  the  condensation  is  made.  At  the  same 
time,  the  "expansion  of  B  causes  a  filling  up  of  the  rarefaction 
at  A,  so  that  this  section  is  restored  to  its  normal  state.  This 
is  not  all :  the  folds  in  the  section  B  do  not  stop  in  their 
swing  when  they  have  recovered  their  original  position,  but, 
like  a  pendulum,  swing  beyond  the  position  of  rest,  thus 
producing  a  rarefaction  at  B,  where  immediately  before  there 
was  a  condensation.  Thus  a  forward  movement  of  the  rare- 
faction is  made,  and  thus  a  pulse  or  wave  is  transmitted  with 
uniform  velocity  through  a  spiral  spring  or  any  elastic 
medium. 

A  wave  cannot  be  transmitted  through  an  inelastic  soft 
iron  spiral.  Elasticity  is  essential  in  a  medium,  that  it  may 
transmit  waves  composed  of  condensations  and  rarefactions  / 
and  the  greater  the  elasticity,  the  greater  the  facility  and 
rapidity  with  which  a  medium  transmits  waves. 

154.    Air  as  a  medium  of  ivave-motion. 

Experiment  4-  —  Place  a  candle  flame  at  the  orifice  a  of  the  long  tin 
tube  A  (Fig.  158)  and  strike  the  table  a  sharp  blow  with  a  book  near  the 


AIK    AS    A    MEDIUM    OF    WAVE-MOTION. 


189 


orifice  &.     Instantly  the  candle  flame  is  quenched.     The  body  of  air  in 
the  tube  serves  as  a  medium  for  transmission  of  motion  to  the  candle. 


FIG.  158. 

Is  the  motion  transferred  that  of  a  current  of  air  through  the  tube  (a 
miniature  wind),  or  is  it  a  vibratory  motion  ?  Burn  touch-paper1  at  the 
orifice  6,  so  as  to  fill  this  end  of  the  tube  with  smoke,  and  repeat  the  last 
experiment. 

Evidently,  if  the  body  of  the  air  be  moved  along  through 
the  tube,  the  smoke  will  be  carried  along  with  it.  The  candle 
is  blown  out  as  before,  but  no  smoke  issues  from  the  orifice  a. 
It  is  clear  that  there  is  no  translation  of  material  particles 
from  one  end  to  the  other,  —  nothing  like  the  flight  of  a  rifle 
bullet.  The  candle  flame  is  struck  by  something  like  &  pulse 
of  air,  not  by  a  wind? 

Air  is  a  fluid,  and  has  therefore  only  volume  elasticity. 
The  only  waves  it  can  propagate  are  waves  composed  of  com- 
pressions and  rarefactions.  In  a  previous  chapter  we  have 
seen  how  a  wave  is  the  result  of  a  transmission  of  harmonic 
motion  or  harmonic  vibrations  through  a  series  of  particles.  A 
sound-wave  consists  of  a  succession  of  particles  of  the  sound 
medium  vibrating  harmonically  and  successively  and  in  the 

1  To  prepare  touch-paper,  dissolve  about  a  teaspoonful  of  saltpetre  in  a  half-tea- 
cupful  of  hot  water,  dip  unsized  paper  in  the  solution,  and  then  allow  it  to  dry.    The 
paper  produces  much  smoke  in  burning,  but  no  flame. 

2  If  a  membrane  be  tied  tightly  over  the  orifice  b  and  a  sudden  blow  be  given  it 
(e.g.  by  snapping  it  with  a  ringer),  the  vibratory  character  of  the  motion  communi- 
cated through  the  tube  is  well  shown  by  the  flame  being  first  driven  from  the  orifice  a 
and  immediately  afterward  drawn  toward  it. 


190  MOLAR    DYNAMICS. 

same  direction  as  that  in  which  the  sound-wave  moves  There 
are  two  important  distinctions  between  these  waves  and  waves 
of  water,  or  waves  sent  along  a  cord  when  one  end  is  shaken  : 
the  former  consist  of  condensations  and  rarefactions  ;  the 
latter  of  elevations  and  depressions.  In  the  former,  the 
vibration  of  the  particles  is  in  the  same  line  with  the  path  of 
the  wave,  and  hence  they  are  called  longitudinal  vibrations  ; 
in  the  latter  the  vibrations  take  place  in  planes  at  some  angle 
to  the  path  of  the  wave,  and  are  therefore  called  transverse 
vibrations. 

Boys  often  amuse  themselves  by  inflating  paper  bags,  and 
with  a  quick  blow  bursting  them,  producing  with  each  a  single 
loud  report.  First  the  air  is  suddenly  and  greatly  condensed 
by  the  blow,  and  the  bag  is  burst;  the  air  now,  as  suddenly 
and  with  equal  force,  expands,  and  by  its  expansion  condenses 
the  air  for  a  certain  distance  all  around  it,  leaving  a  rare- 
faction where  just  before  had  been  a  condensation.  If  many 
bags  were  burst  at  the  same  spot  in  rapid  succession,  the 
result  would  be  that  alternating  shells  of  condensation  and 
rarefaction  would  be  thrown  off,  all  having  a  common  center, 
enlarging  as  they  advance,  as  do  the  ripples  formed  by  stones 
dropped  into  water ;  except  that,  in  this  case,  the  waves  are 
not  like  rings,  but  hollow  globes ;  not  circular,  but  spherical. 
In  this  manner  sound-waves  produced  by  the  vibration  of  a 
sounding  body  travel  through  the  air. 

As  a  wave  advances,  each  individual  air-particle  concerned 
in  its  transmission  performs  a  short  excursion  to  and  fro  in 
the  direction  of  a  straight  line  radiating  from  th«  center  of 
the  shells  or  hollow  globes.  A  sound-wave  travels  its  own 
length  in  the  time  that  a  particle  occupies  in  going  through  one 
complete  vibration  so  as  to  be  ready  to  start  again. 

Experiment  5.  —  Take  a  strip  of  black  cardboard  4.5  inches  X  1  inch. 
Cut  a  slit  about  one-sixteenth  of  an  inch  wide  lengthwise  and  centrally 
through  the  strip  nearly  from  end  to  end,  Place  the  slit  across  the  page 


NATURE   OF    SOUND   AND    SOUND-WAVES. 


191 


just  below  Fig.  159,  and  draw  the  book  along  underneath  in  the  direction 
of  the  arrow.  Imagine  that  the  short  dark  dashes  seen  through  the  slit 
represent  a  series  of  air-particles,  and  the  slit  itself  represents  the  direc- 
tion in.  which  a  series  of  sound-waves  is  travelling.  It  will  be  seen  that 


FIG. 159. 


each  air-particle  moves  a  little  to  and  fro  in  the  direction  in  which  the 
sound-waves  travel,  and  comes  back  to  its  starting-point ;  but  the  conden- 
sations and  rarefactions,  represented  by  a  group  (half  a  wave-length)  of 
dots  becoming  alternately  closer  together  or  farther  apart,  are  transmitted 
through  the  whole  series  of  air-particles. 

155.  Nature  of  sound  and  sound-waves.  —  Sound  is  a  sen- 
sation caused  usually  by  air-waves  beating  upon  the  organ  of 
hearing.1 

1  As  commonly  used  the  term  sound  is  ambiguoiis,  being  applied  to  both  a 
sensation  and  the  physical  cause  of  the  sensation.  In  a  scientific  treatise  ambiguity 
and  consequent  confusion  are  disastrous.  No  apology,  therefore,  is  required  for 
restricting  the  term  to  its  legitimate  signification.  With  sound  itself  we  have  little 


192  MOLAR    DYNAMICS. 

Sound-waves  are  ivaves  in  any  medium  (usually  air)  that  are 
capable  of  producing  the  sensation  of  sound.  A  body  vibrating 
in  an  elastic  medium,  e.g.  in  air,  does  not  necessarily  produce 
sound-waves  ;  in  other  words  not  all  waves  are  sound-waves. 
For  example,  the  energy  of  the  vibrations  may  be  insufficient, 
or  the  vibrating  body  may  be  so  small  (or  the  medium  so 
rare)  that  it  cuts  through  the  medium  without  condensing  it 
sufficiently  to  produce  audible  effects. 

156.  Solids  and  liquids  are  media  capable  of  transmitting 
sound-waves. 

Experiment  6.  —  Lay  a  watch,  with  its  back  downward,  on  a  long 
board  (or  table),  near  to  one  of  its  ends,  and  cover  the  watch  with  loose 
folds  of  cloth  until  its  ticking  cannot  be  heard  through  the  air  in  any 
direction  at  a  distance  equal  to  the  length  of  the  board.  Now  place  the 
ear  in  contact  with  the  farther  end  of  the  board,  and  you  will  hear  the 
ticking  of  the  watch  very  distinctly. 

Experiment  7..  —  Place  one  end  of  a  long  pole  on  a  cigar  box,  and 
apply  the  stem  of  a  vibrating  tuning-fork  to  the  other  end ;  the  sound- 
vibrations  will  be  transmitted  through  the  pole  to  the  box,  and  a  sound 
will  be  given  out  by  the  box,  as  though  that,  and  not  the  tuning-fork, 
were  the  origin  of  the  sound. 

Experiment  8.  — Place  the  ear  to  the  earth,  and  listen  to  the  rumbling 
of  a  distant  carriage  ;  or  put  the  ear  to  one  end  of  a  long  stick  of  timber, 
and  let  some  one  gently  scratch  the  other  end  with  a  pin. 


SECTION  II. 

SPEED    OF    SOUND-WAVES. 

157.  Speed  of  sound-waves  dependent  on  elasticity  and  den- 
sity of  medium.  —  It  may  be  demonstrated 1  that  in  siuqile 
harmonic  motion,  the  velocity  with  which  a  particle  of  an  elastic 

to  do,  as  this  is  a  physiological  rather  than  a. physical  phenomenon.    No  more 
appropriate  name  than  sound-wave  can  be  applied  to  the  physical  agent  Avith  which 
we  are  to  deal ;  it  suggests  at  once  the  reality,  and  is  not  suggestive  of  some  vague 
mysterious  thing  shot  through  space. 
i  See  Barker's  Physics,  p.  219. 


SPEED    OF    SOUND-WAVES.  193 

medium  vibrates,  and  therefore  the  speed  of  propagation  in  the 
medium  (hence,  the  speed  of  a  sound-wave),  is  directly  propor- 
tional to  the  square  root  of  the  elasticity  of  the  medium,  and 
inversely  proportional  to  the  square  root  of  its  density.  The 
relation  of  these  quantities  is  shown  in  the  formula 


If  the  elasticity  and  density  of  the  medium  vary  alike,  and 
in  the  same  direction,  it  is  evident  that  the  speed  of  the 
sound-wave  is  unaffected.  Hence  the  speed  of  a  sound-wave 
is  unaffected  by  barometric  hight,  or  elevation  above  sea-level. 
Temperature,  however,  affects  only  the  density  of  air.  Ele- 
vation of  temperature  of  the  air  diminishes  the  density  of  the 
air,  and  therefore  tends  to  increase  the  speed  of  the  sound- 
wave. Moisture  in  the  air  renders  it  less  dense  (pressure 
remaining  constant),  and  thereby  tends  to  increase  the  speed. 
The  velocity  of  a  sound-wave  is  greatest  in  the  direction  of 
the  wind.  Speed  of  sound-waves  is  very  nearly  independent 
of  pitch  and  intensity. 

The  greater  density  of  solids  and  liquids,  as  compared  with 
gases,  tends,  of  course,  to  diminish  the  speed  of  sound-waves; 
but  their  greater  incompressibility  more  than  compensates 
for  the  decrease  of  speed  occasioned  by  the  increase  of  den- 
sity. As  a  general  rule,  solids  are  more  incompressible  than 
liquids  ;  hence  sound-waves  generally  travel  faster  in  the 
former  than  in  the  latter.  For  example,  sound-waves  travel 
in  water  about  four  times  as  fast  as  in  air,  and  in  iron  and 
glass  sixteen  times  as  fast. 

The  speed  of  sound-waves  in  free  air  at  0°  C.  is  332.4  m 
(nearly  1091  ft.)  per  second.  The  increase  of  speed  per 
degree  C.  is  .608  m  (23.9  in.).  The  speed  in  other  gases  — 

v 
—j=-,  in  which  v  is  the  speed  in  air  and  d  the  density  of  the 

given  gas  referred  to  air.     For  example,  in  hydrogen,  whose 


194  MOLAR    DYNAMICS. 

density  is  ^  that  of  air,  the  speed  at  0°  C.  is  about  4163  ft. 
per  second.  The  speed  of  sound-waves  in  any  medium  may 
be  calculated  from  the  formula  given  above  and  by  experi- 
mental methods  to  be  given  further  on. 


SECTION  III. 

ENERGY    OF    SOUND-WAVES.       LOUDNESS. 

158.  Energy  of  sound-waves  depends  on  the  amplitude  of 
vibration.  —  Gently  tap  the  prongs  of  a  tuning-fork  and  dip 
them  into  water,  —  the  water  is  scarcely  moved  by  them  ; 
increase  the  energy  of  the  blow,  — -.  the  vibrations  become 
wider,  and  the  water  spray  is  thrown  with  greater  force  and 
to  a  greater  distance.  The  same  thing  occurs  when  the  fork 
vibrates  in  the  air ;  though  we  do  not  see  the  air-particles  as 
they  are  batted  by  the  moving  fork,  yet  we  feel  the  effects 
as  a  sound  sensation,  and  we  judge  of  their  energy  by  the 
intensity  of  the  sensation  which  they  produce. 

Fix  your  attention  upon  a  particle  of  air  as  a  sound-wave 
passes  it.  A  harmonic  motion  is  impressed  upon  it.  At  a 
certain  point  of  its  excursion  its  velocity  is  at  its  maximum. 
Now  since  the  energy  of  a  moving  particle  varies  as  the 
square  of  its  velocity,  the  intensity  of  the  impact  which  it  is 
capable  of  producing  upon  the  tympanum  of  the  ear  is  propor- 
'  tional  to  the  square  of  this  maximum  velocity. 

It  is  also  clear  that  if  the  amplitude  of  vibration  of  a 
particle  be  doubled  while  its  period  remains  constant,  its 
velocity  is  doubled,  and  therefore  its  energy  is  increased  four- 
fold. Hence,  (1)  measured  mechanically,  the  energy  of  a 
sound-wave  is  proportional  to  the  square  of  the  amplitude  of  the 
vibration  of  particles,  or,  it  is  proportional  to  the  square  of  the 
maximum  velocity  of  the  vibrating  particles.  An  amplitude  of 
less  than  yirinnrwinT  cm  *s  sufficient  to  cause  hearing. 


ENERGY   OF    SOUND-WAVES.  195 

Loudness  of  sound  refers  to  the  intensity  of  a  sensation. 
We  have  no  standard  of  measurement  for  a  sensation,  so  we 
are  compelled  to  measure  the  energy  of  the  sound-wave, 
knowing  at  the  same  time  that  loudness  is  not  proportional  to 
this  energy. 

159.  Energy  of  sound-waves  depends  upon  the  density  of 
the  medium.  —  In  the  experiment  with  the  watch  under  the 
receiver  of  the  air-pump  (p.  187),  the  sound  grew  feebler  as 
the  air  became  rarer.     Aeronauts  are  obliged  to  exert  them- 
selves   more   to   make  their  conversation  heard  when  they 
reach  great  hights  than  when  in  the  denser  lower  air.      In 
diving-bells  persons  are  obliged  to  speak  in  undertones.     In  a 
rare  medium  a  vibrating  body  during  a  single  vibration  either 
sets  in  motion  fewer  particles,  as  in  the  case  of  the  partially 
exhausted  receiver,  or,  as  in  the  case  of  hydrogen  gas,  it  sets 
in  motion  particles  of  less  mass  than  in  a  dense  medium  ; 
consequently  it  parts  with  its  energy  more  slowly,  and  the 
sound  is  consequently  weaker. 

(2)  The  energy  of  gaseous  sound-waves  increases  with  the 
density  of  the  medium  in  which  they  are  produced. 

160.  Energy  of  sound-waves  depends  on  distance  from  their 
source.  —  It  is  a  matter  of  every-day  observation  that  the 
loudness  of  a  sound  diminishes  very  rapidly  as  the  distance 
from  the  source  of  the  waves  to  the  ear  increases.      As  a 
sound-wave   advances   in    an   ever-widening  sphere,   a  given 
quantity  of  energy  becomes  distributed  over  an  ever-increasing 
surface  ;  and  as  a  greater  number  of  particles  partake  of  the 
motion,  the  individual  particles  receive  proportionately  less 
energy  ;  hence  it  follows,  —  as  a  consequence  of  the  geomet- 
rical truth,  that  "  the  surface  of  a  sphere  varies  as  the  square 
of  its  radius," -  —  that   (3)   the  energy  of  a  sound-wave  varies 
inversely  as  the  square  of  the  distance  from,  the  source.     This  is 
known  as  the  Law  of  Inverse  Squares.1     For  example,  if  two 

1  That  the  Law  of  Inverse  Sqtiares  is  applicable  to  sound-waves  is  sometimes 


196  MOLAR   DYNAMICS. 

persons,  A  and  B,  be  respectively  500  and  1000  rods  from  a 
gun  when  it  is  discharged,  the  waves  that  reach  A  will  have 
four  times  the  energy  that  the  same  waves  have  when  they 
reach  B. 

161.  Speaking-tubes. 

Experiment  9.  —  Place  a  watch  at  one  end  of  the  long  tin  tube  (Fig. 
158),  and  the  ear  at  the  other  end.  The  ticking  sounds  very  loud,  as 
though  the  watch  were  close  to  the  ear. 

Long  tin  tubes,  called  speaking-tubes,  passing  through  many 
apartments  in  a  building,  enable  persons  at  the  distant  ex- 
tremities to  carry  on  conversation  in  a  low  tone  of  voice, 
while  persons  in  the  various  rooms  through  which  the  tube 
passes  hear  little  or  nothing.  The  reason  is  that  the  sound- 
waves which  enter  the  tube  are  prevented  from  expanding, 
consequently  the  energy  of  the  sound-waves  is  not  affected  by 
distance,  except  as  it  is  wasted  by  friction  of  the  air  against 
the  sides  of  the  tube,  and  by  internal  friction  due  to  the 
viscosity  of  the  air. 

162.  Energy  of  sound-waves  depends  on  the  homogeneousness 
of  the  transmitting  medium.  —  Observations  and  experiments  of 
Humboldt,  Tyndall,  and  Henry  have  established  the  following 
facts  :  Rain,  hail,  snow,  and  fog  offer  little  or  no  obstruction 
to  the  passage  of  a  sound-wave.     The  air  associated  with  a 
fog  is,  as  a  general  rule,  highly  homogeneous  and  favorable 
to  the  transmission  of  sound.    An  atmosphere  optically  opaque 
may  be  acoustically  transparent,  and  vice  versa  ;  hence  the 
great  value  of  fog  horns.     Streams  of  air  differently  heated, 
or  saturated  in  different  degrees  with  aqueous  vapor,  though 
invisible  to  the  eye,  form  acoustic  clouds  which  may  greatly 
interfere  with  the  propagation  of  sound-waves. 

163.  Energy  of  sound-waves   affected   by   winds.  —  It   not 
infrequently  happens  that  sound-waves   are  audible  two  or 

called  in  question.  For  an  experimental  demonstration  of  its  applicability,  see 
"  Contributions  from  the  Physical  Laboratory,  Mass.  Inst.  Technology,  1876." 


REFLECTION    OF    SOUND-WAVES. 


197 


three  times  as  far  to  the  leeward  as  to  the  windward.  Sound- 
waves are  borne  along  with  the  wind,  but,  of  course,  are 
impeded  by  it  when  the  directions  of  their  motions  are  opposed 
to  it. 

SECTION  IV. 

CHANGES    IN    DIRECTION    OF    PROPAGATION    OF    SOUND-WAVES. 

164.  Reflection.  —  So  long  as  sound-waves  are  not  ob- 
structed in  their  motion  they  are  propagated  in  the  form  of 
concentric  spheres  ;  but  when  they  meet  with  an  obstacle, 
they  follow  the  general  law  of  elastic  bodies;  that  is,  they 
return  upon  themselves,  forming  new  concentric  waves,  called 
reflected  waves,  which  seem  to  emanate  from  a  second  center 
on  the  other  side  of  the  reflecting  body.  This  phenomenon 
is  called  the  reflection  of  sound-waves.  A  (Fig.  160)  repre- 
sents a  vibrating  particle  or  a  sonorous  center  from  which 


emanates  a  series  of  waves.  P  Q  represents  an  obstacle  with 
a  flat  surface  turned  toward  the  waves.  Take,  for  example, 
the  incident  wave  MCDN,  emitted  from  the  center  A  ;  the 
corresponding  reflected  wave  is  represented  by  the  arc  C  K  D 


198  MOLAR   DYNAMICS. 

of  a  circle  whose  center  a  is  as  far  beyond  the  obstacle  P  Q 
as  A  is  in  front  of  it. 

Join  any  point,  C,  of  the  reflecting  surface  to  the  sonorous 
center,  and  the  line  A  C  represents  one  of  an  infinite  number 
of  directions  in  which  energy  is  transmitted  by  a  sound-wave. 
Such  a  line  may  conveniently  be  called  a  sound-ray.  Let  fall 
the  line  HC  normal  to  the  surface  at  the  point  of  incidence  C. 
The  angle  A  C  H  is  called  the  angle  of  incidence.  The  ray 
A  C  after  reflection  takes  the  direction  C  B,  which  is  a  prolon- 
gation of  «C.  The  angle  BCH  is  called  the  angle  of  reflection, 
An  observer  at  B  receives  sound-waves  not  only  directly  from 
A  in  the  line  AB,  but  also  from  C  in  the  line  CB.  Hence  he 
hears  two  sounds,  one  (to  speak  in  common  parlance)  proceed- 
ing from  point  A,  and  the  other  from  point  C.  The  latter 
travels  from  A  to  C  and  from  C  to  B,  a  longer  distance  than 
AB,  and  is  therefore  heard  later  than  the  former.  If  the 
interval  of  time  between  their  arrivals  at  B  be  greater  than 
about  a  fifth  of  a  second,  the  ear  is  able  to  separate  the  two 
sensations  and  the  latter  appears  as  an  echo.  If  the  interval 
of  time  be  too  short,  then  only  a  single  and  perhaps  somewhat 
blurred  and  indistinct  sound  is  heard.  The  latter  phenomenon 
is  usually  called  resonance.  Such  an  effect  is  experienced 
frequently  by  a  person  listening  to  his  own  voice  in  a  large 
hall. 

If  the  obstacle  PQ  present  a  concave  surf  ace, -the  wave- 
front  after  reflection  will  be  less  convex,  and  may  become 
plane  or  even  concave  according  to  the  degree  of  the  concavity 
of  the  reflector  and  the  position  of  the  sounding  body. 

165.    Sound-waves  reflected  by  concave  mirrors. 

Experiment.  —  Place  a  watch  at  the  focus  A  (Fig.  161)  of  a  concave 
mirror  G.  At  the  focus  B  of  another  concave  mirror  H,  place  the  large 
opening  of  a  small  tunnel,  and  with  a  rubber  connector  attach  the  bent 
glass  tube  C  to  the  nose  of  the  tunnel.  The  extremity  D  being  placed 
in  the  ear,  the  ticking  of  the  watch  can  be  heard  very  distinctly,  as  though 


REFRACTION   OF   SOUND-WAVES.  199 

it  were  somewhere  near  the  mirror  H.     Though  the  mirrors  be  12  feet 
apart,  the  sound  will  be  louder  at  B  than  at  an  intermediate  point  E. 

How  is  this  explained?  Every  air-particle  in  a  certain 
radial  line,  as  Ac,  receives  and  transmits  motion  in  the 
direction  of  this  line ;  the  last  particle  strikes  the  mirror 


elastic,  bounds  off  in  the 
direction  c  c',  communicat-   >fl 
ing  its  motion  to  the  par- 
ticles in  this  line.     At  c' 
a  similar  reflection  gives    ' 
motion  to  the  air  particles 

I/ 

\0     II 

4: 

R    /V 

A        E     ^Eg|3b. 

V 

(f     vF 

c\ 

cl     1 

D 
FIG.  161. 

in  the  line  c'B.  In  consequence  of  these  two  reflections,  all 
divergent  sound-rays,  as  A^,  Ae,  etc.,  that  meet  the  mirror  G, 
are  there  rendered  parallel,  and  afterwards  rendered  conver- 
gent at  the  mirror  H.  The  practical  result  of  the  concentra- 
tion of  this  scattering  energy  is,  that  a  sound  of  great  intensity 
is  heard  at  B.  The  points  A  and  B  are  called  the  foci  of  the 
mirrors.  The  front  of  the  wave  as  it  leaves  A  is  convex,  in 
passing  from  G  to  H  it  is  plane,  and  from  H  to  B  concave. 
If  you  fill  a  large  circular  tin  basin  with  water,  and  strike 
one  edge  with  a  knuckle,  circular  waves  with  concave  fronts 
will  close  in  on  the  center,  heaping  up  the  water  at  that  point. 

Long  "  whispering-galleries  "  have  been  constructed  on  this 
principle.  Persons  stationed  at  the  foci  of  the  concave  ends 
of  the  long  gallery  can  carry  on  a  conversation  in  a  whisper 
which  persons  between  cannot  hear.  The  external  ear  is  a 
wave-condenser.  The  hand  held  concave  behind  the  ear,  by 
its  increased  surface,  adds  to  its  efficiency. 

166.  Refraction.  —  If  you  place  your  ear  at  the  small  end 
of  a  tunnel,  C  (Fig.  162),  and  listen  to  the  ticking  of  a  watch, 
A,  about  4  meters  distant,  and  then  introduce  a  collodion 
balloon,  B,  filled  with  carbonic  acid  gas  between  your  ear 


200 


MOLAR    DYNAMICS. 


and  the  watch,  and  very  near  the  latter,  the  sound  becomes 
louder. 

The  cause  is  obvious  :   for  let  the  curved  lines  a,  b,  c,  etc., 
represent  sections  of  sound-waves  with  convex  fronts,  and  B 


FIG.  162. 

a  spherical  body  of  carbonic  acid  gas  which  is  denser  than  air  ; 
then  it  is  clear  that,  owing  to  the  slower  progress  of  the  waves 
in  the  denser  gas,  they  would  become  flattened  on  entering 
this  gas,  and  the  waves  of  convex  fronts  may  be  changed  to 
waves  of  plane  fronts.  Again,  points  at  the  extremities  of 
the  waves,  having  less  distance  to  travel  in  the  denser  gas 
than  points  near  the  center,  would  emerge  first  and  get  in 
advance,  and  thus  the  wave  fronts  which  are  plane  or  nearly 
so  while  wholly  in  the  dense  gas,  become  concave  on  leaving 
it.  By  these  changes  in  the  form  of  the  wave  fronts,  sound 
energy  which  was  originally  becoming  diffused  through  wider 
and  wider  space,  and  therefore  becoming  less  intense  as  it 
progressed,  is  so  changed  in  direction  in  passing  into  and  out 
of  a  medium  of  greater  density,  that  the  energy  is  finally 
concentrated  at  a  distant  point,  as  at  C,  and  thereby  inten- 
sified. 

Any  change  in  direction  of  sound,  caused  by  passing  from 
a  medium  of  a  certain  density  into  a  medium  of  different 
density,  is  called  refraction. 

167.  Diffraction. — When  sound-waves  encounter  an  ob- 
stacle, a  series  of  secondary  waves  are  formed  with  the  edges 


REENFORCEMENT    OF    SOUND-WAVES. 


201 


of  the  obstacle  as  centers.  These  waves  appear  to  flow  around 
behind  the  object,  so  that  the  obstacle  is  able  to  produce  only 
a  partial  sound-shadow.  " Sounds  heard  around  a  corner" 
are  thus  accounted  for.  This  bending,  as  it  were,  of  waves 
around  an  obstacle  is  called  diffraction. 


SECTION  V. 

REENFORCEMENT    OF    SOUND-WAVES  ;     INTERFERENCE    OF 
SOUND-WAVES. 

168.  Reinforcement  of  sound-waves. 

Experiment  1.  —  Set  a  diapason  in  vibration  ;  you  can  scarcely  hear 
the  sound  unless  it  is  held  near  the  ear.  Press  the  stem  against  a  table  ; 
the  sound  rings  out  loud,  but  the  waves  seem  to  proceed  from  the  table. 

When  only  the  fork  vibrates,  the  prongs,  presenting  little 
surface,  cut  their  way  through  the  air,  producing  very  slight 
condensations,  and  consequently  waves  of  little  intensity. 
When  the  fork  rests  upon  the  table,  the  vibrations  are  com- 
municated to  the  table ;  the  table  with  its  larger  surface 
throws  a  larger  mass  of  air 
into  vibration,  and  thus 
greatly  intensifies  the  sound- 
waves. The  strings  of  the 
piano,  guitar,  and  violin  owe 
as  much  of  their  loudness  of 
sound  to  their  elastic  sound- 
ing-boards as  the  fork  does 
to  the  table. 

169.  Reinforcement  by  bod- 
ies of  air ;  resonators. 


Experiment  2.  —  Take  a  glass 
tube,  A  (Fig.  163),  16  inches  long 
and  2  inches  in  diameter ;  thrust  one  end  into  a  vessel  of  water,  C,  and 
hold  over  the  other  end  a  vibrating  diapason,  B,  that  makes  (say)  256 


202  MOLAR   DYNAMICS. 

vibrations  in  a  second.  Gradually  lower  the  tube  into  the  water,  and 
when  it  reaches  a  certain  depth,  i.e.  when  the  column  of  air  oc  attains  a 
certain  length,  the  sound  becomes  very  loud ;  as  the  tube  is  lowered 
below  this  point,  the  sound  rapidly  dies  away. 

Columns  of  air,  as  well  as  sounding-boards,  serve  to  reenforce 
sound-waves.  The  instruments  which  enclose  the  columns  of 
air  are  called  resonators.  Unlike  sounding-boards,  they  can 
respond  loudly  to  only  one  tone,  or  to  a  few  tones  of  widely 
different  pitch. 

How  is  this  reenforcement  effected?  When  the  prong  a 
moves  from  one  extremity  of  its  arc  a'  to  the  other  a",  it 
sends  a  condensation  down  the  tube ;  this  condensation, 
striking  the  surface  of  the  water,  is  reflected  by  it  up  the 
tube.  Now  suppose  that  the  front  of  this  reflected  conden- 
sation should  just  reach  the  prong  at  the  instant  it  is  starting 
on  its  retreat  from  a"  to  a' ;  then  the  reflected  condensation 
will  conspire  with  the  condensation  formed  by  the  prong  in 
its  retreat  to  make  a  greater  condensation  in  the  air  outside 
the  tube.  Again,  the  retreat  of  the  prong  from  a"  to  a' 
produces  in  its  rear  a  rarefaction,  which  also  runs  down  the 
tube,  is  reflected,  and  will  reach  the  prong  at  the  instant  it  is 
about  to  return  from  a'  to  a",  and  to  cause  a  rarefaction  in  its 
rear ;  these  two  rarefactions  moving  in  the  same  direction 
conspire  to  produce  an  intensified  rarefaction.  The  original 
sound-waves  thus  combine  with  the  reflected,  to  produce 
resonance  ;  but  this  can  happen  only  when  the  like  parts  of 
each  wave  coincide  each  with  each  ;  for  if  the  tube  were 
somewhat  longer  or  shorter  than  it  is,  it  is  plain  that  conden- 
sations and  rarefactions  would  meet  in  the  tube,  and  tend  to 
destroy  each  other. 

The  loudness  of  sound  of  all  wind  instruments  is  due  to 
the  resonance  of  the  air  contained  within  them.  A  simple 
vibratory  movement  at  the  mouth  or  orifice  of  the  instrument, 
scarcely  audible  in  itself  (such  as  the  vibration  of  a  reed  in 


MEASURING   LENGTHS    OF    SOUND-WAVES. 


203 


reed  pipes,  or  a  pulsatory  movement  of  the  air,  produced  by 
the  passage  of  a  thin  sheet  of  air  over  a  sharp  wooden  or 
metallic  edge,  as  in  organ  pipes,  flutes,  and  flageolets,  or  more 
simply  still  by  the  friction  of  a  gentle  stream  of  breath  from 
the  lips  sent  obliquely  across  the  open  end  of  a  closed  tube 
or  pen-case),  is  sufficient  to  set  the  large  body  of  enclosed  air 
in  the  instrument  into  vibration,  and  the  sound  thus  reenforced 
becomes  audible  at  long  distances. 

Experiment  3.  —  Attach  a  rose  gas-burner,  A  (Fig.  164),  to  a  metal 
gas-tube  about  1  m  in  length,  and  connect  this  by  a 
rubber  tube  with  a  gas-nipple.  Light  the  gas  at  the 
rose  burner,  and  you  will  hear  a  low,  rustling  noise. 
Remove  the  conical  cap  from  the  long  tin  tube  (Fig. 
158),  support  the  tube  in  a  vertical  position,  and  gradu- 
ally raise  the  burner  into  the  tube  ;  when  it  reaches  a 
certain  point  not  far  up,  the  body  of  air  in  the  tube  will 
catch  up  the  vibrations,  and  ^give  out  deafening  sound- 
waves that  will  shake  the  walls  and  furniture  in  the 
room. 

170.  Measuring  ivave-lengths  and  the  speed 
of  sound-waves.  —  Experiments  like  that  de- 
scribed on  p.  201  enable  us  readily  to  meas- 
ure the  length  of  the  wave  produced  by  a  fork 
whose  vibration  number  is  known,  and  also  to 
measure  the  velocity  of  sound-waves.  It  is 
evident  that  if  a  condensation  generated  by 
the  prong  of  the  fork  in  its  forward  movement  from  a'  to  a" 
(Fig.  163)  meet  with  no  obstacle,  its  front,  meantime,  will 
traverse  the  distance  od,  or  twice  the  distance  oc;  hence  the 
length  of  the  condensation  is  the  distance  od.  But  a  conden- 
sation is  only  one-half  of  a  wave,  and  the  passage  of  the 
prong  from  a'  to  a"  is  only  one-half  of  a  vibration  ;  conse- 
quently the  distance  od  is  one-half  of  a  wave-length,  and  the 
distance  ocis  one-fourth  of  a  wave-length.  The  measured  dis- 
tance of  oc  in  this  case  is  about  13.13  inches  ;  hence  the 


FIG.  164. 


204 


MOLAlt    DYNAMICS. 


length  of  wave  produced  by  a  C'-fork  making  256  vibrations 
in  a  second  is  (13.13  inches  X  4  =)  52.5  inches  —  4.38  feet. 
And  since  a  wave  from  this  fork  travels  4.38  feet  in  ^1^  of  a 
second,  it  will  travel  in  an  entire  second  (4.38  feet  X  256  — ) 
1121  feet.  The  distance  oc  varies  with  the  temperature  of 
the  air. 

It  is  evident  that  the  three  quantities  expressed  in  the 
formula 

velocity 

wave-length  = — ^ — - — 

number  of  vibrations 

bear  such  a  relation  to  one  another  that  if  any  two  be  known, 
the  remaining  quantity  can  be  computed.  It  will  further  be 
observed  that  with  a  given  velocity  the  wave-length  varies 
inversely  as  the  number  of  vibrations  ;  i.e.  the  greater  the  num- 
ber of  vibrations  per  second,  the  shorter  the  wave-length. 
171.  Interference  of  sound-waves. 

Experiment  4.  —  Hold  a  vibrating  diapason  over  a  resonance-jar,  as  in 

Fig.  165.  Roll  the  diapason  over 
slowly  in  the  fingers.  At  certain 
points  a  quarter  of  a  revolution 
apart,  when  the  diapason  is  in  an 
oblique  position  with  reference  to 
the  edge  of  the  jar  as  represented 
in  the  figure,  the  reenforceinent 
from  the  tube  almost  entirely  dis- 
appears, but  it  reappears  at  the  in- 
termediate points.  That  is,  there 
are  four  intervals  in  the  space 
around  the  fork  where  the  two 
series  of  waves  generated  by  the 
two  tines  interfere  to  produce 
mutual  destruction.  These  are 
called  technically  the  cones  of  silence.  Keturn  to  the  position  where 
there  is  no  resonance,  and  enclose  in  a  loose  roll  of  paper  the  prong 
farthest  from  the  tube,  without  touching  the  diapason,  so  as  to  prevent 
the  sound-waves  produced  by  that  prong  from  passing  into  the  tube;  the 


FIG.  165. 


FORCED    AND    SYMPATHETIC    VIBRATIONS. 


205 


resonance  resulting  from  the  vibrations  of  the  other  prong  immediately 
appears. 

Experiment  5.  —  Select  two  of  the  tubes  (Fig.  188)  of  nearly  the  same 
length,  blow  through  them,  and  notice  the  peculiar  throbbing  sound 
produced  by  the  interference  of  the  two  sounds. 

Experiment  6.  —  Stop  one  of  the  orifices  of  a  bicyclist's 
whistle  (Fig.  166),  and  sound  one  whistle  at  a  time.  The 
sound  of  each  is  clear  and  smooth.  Sound  both  whistles  at 
the  same  time,  and  you  obtain  the  usual  rough  and  discord- 
ant sound. 

The  two  whistles  of  unequal  length  give  out  waves  of 
slightly  different  length,  so  that  at  certain  short  intervals 
both  waves  will  interfere  in  the  same  phase  (i.e.  condensation 
with  condensation)  and  produce  intensified  sounds  which 
are  heard  at  long  distances,  while  at  other  intervals  they 
interfere  in  opposite  phases  (i.e.  condensation  with  rarefac- 
tion), and  the  result  of  their  mutual  destruction  is  to  cause 
the  otherwise  smooth  sound  to  become  broken  or  rattling. 

Two  sound-waves  may  combine  to  produce  a  sound  louder 
or  weaker  than  either  alone  would  produce,  or  may  even  cause 
silence.     This  combination  of  sound-waves  to  produce  a  louder  or  weaker 
sound  is  called  interference. 

172.    forced  and  sympathetic  vibrations. 


FIG.  166. 


Experiment  7. 


Suspend  from  a  frame  several  pendulums,  A,  B,  C, 
etc.  (Fig.  167).  A  and  D  are  each  3  feet  long, 
C  is  a  little  longer,  and  B  and  E  are  shorter. 
Set  A  in  vibration,  and  slight  impulses  will  be 
communicated  through  the  .frame  to  D,  and 
cause  it  to  vibrate.  The  vibration-period  of  D 
being  the  same  as  that  of  A,  all  the  impulses 
tend  to  accumulate  motion  in  D,  so  that  it  soon 
vibrates  through  arcs  as  large  as  those  of  A. 
On  the  other  hand,  C,  B,  and  E,  having  differ- 
ent rates  of  vibration  from  that  of  A,  will  at 
first  acquire  a  slight  motion,  but  soon  their 
vibrations  will  be  in  opposition  to  those  of  A, 

and  then  the  impulses  received  from  A  will  tend  to  destroy  the  slight 

motion  they  had  previously  acquired. 

Experiment  8.  —  Press  down  gently  one  of  the  keys  of  a  piano  so  as  to 


c 
FIG.  167. 


206 


MOLAR    DYNAMICS. 


raise  the  damper  without  making  any  sound,  and  then  sing  loudly  into 
the  Instrument  the  corresponding  note.  The  string  corresponding  to  this 
note  will  be  thrown  into  vibrations  that  can  be  heard  for  several  seconds 
after  the  voice  ceases.  If  another  note  be  sung,  this  string  will  respond 
only  feebly. 

Kaise  the  dampers  from  all  the  strings  of  the  piano  by  pressing  the 
foot  on  the  right-hand  pedal,  and  sing  strongly  some  note  into  the  piano. 
Although  all  the  strings  are  free  to  vibrate,  only  those  will  respond  loudly 
that  correspond  to  the  note  you  sing,  i.e.  those  that  are  capable  of  making 
the  same  number  of  vibrations  per  second  as  are  produced  by  your  voice. 
Experiment  9.  — Take  two  forks,  A  and  B  (Fig.  168),  tuned  exactly  in 

unison,  and  mounted  on  reso- 
nance-boxes, and  place  them 
from  three  to  ten  meters  apart. 
Fasten,  by  a  bit  of  sealing-wax, 
a  thread  to  a  thin  piece  of  glass 
12  mm  square  (glass  used  for 
microscopic  mountings  is  the 
best,  or  a  piece  of  photographic 

FlG  16g  tintype  plate  will  answer  well), 

and  suspend  so  as  to  touch  a 

corner  of  one  of  the  prongs  of  the  fork  B.  Set  the  fork  A  in  vibration 
by  drawing  a  resined  bass-viol  bow  strongly  across  the  ends  of  its  prongs. 
In  about  ten  seconds  stop  the  vibrations  of  A  with  the  ringers,  and  you 
will  see  and  hear  the  piece  of  glass  rattling  against  the  prong  of  the  fork 
B';  remove  the  glass,  and  place  the  ear  near  the  fork  B,  or  better,  the 
open  end  of  the  box,  and  you  may  hear  a  distinct  sound,  showing  that 
the  fork  B  has  been  thrown  into  a  state  of  vibration  by  the  fork  A. 

So  the  pulses  that  traverse  the  air  between  the  forks,  so 
gentle  that  only  the  sensitive  organ  of  the  ear  can  perceive 
them,  become  great  enough  to  move  the  rigid  steel  when  the 
energy  of  their  blows,  dealt  at  the  rate  of  perhaps  512  in  a 
second,  accumulates.  The  large  number  of  blows  makes  up 
for  the  feebleness  of  the  individual  blows. 

These  experiments  show  that  a  vibrating  body  tends  to 
make  other  bodies  near  it  vibrate,  even  if  their  periods  of 
vibrations  be  different.  Vibrations  of  this  kind,  such,  for 
example,  as  those  of  B,  C,  and  E  in  Exp.  7  and  those 


PITCH    OF    MUSICAL   SOUNDS. 


207 


generated  in  the  sounding-boards  of  pianos,  violins,  etc.,  are 
called  forced  vibrations.  But  if  the  period  of  the  incident 
waves  of  air  be  the  same  as  that  of  the  body  which  they 
cause  to  vibrate,  the  amplitude  and  intensity  of  the  vibrations 
become  very  great,  like  that  of  the  pendulum  D,  and  those  of 
the  piano  strings  which  gave  forth  the  loud  sounds.  Such 
are  called  sympathetic  vibrations. 


SECTION  VI. 

PITCH    OF    MUSICAL    SOUNDS. 

173.    On  what  pitch  depends. 

Experiment  1.  —  Draw  the  finger-nail  or  a  card  slowly,  and  then 
rapidly,  across  the  teeth  of  a  comb.  The  two  sounds  produced  are  com- 
monly described  as  low  or  grave,  and  high  or  acute.  The  hight  of  a 
musical  sound  is  its  pitch. 

Experiment  2.  —  Cause  the  circular 
sheet-iron  disk  A  (Fig.  169)  to  rotate, 
and  hold  a  corner  of  a  visiting-card  so 
that  at  each  hole  an  audible  tap  shall  be 
made.  Notice  that  when  the  separate 
taps  or  noises  cease  to  be  distinguishable, 
the  sound  becomes  musical ;  also,  that 
the  pitch  of  the  musical  sound  depends 
upon  the  rapidity  of  the  rotation,  i.e. 
upon  the  frequency  of  the  taps. 

Experiment  3.  —  Hold  the  orifice  of  a 
tube  B  so  as  to  blow  through  the  holes 
as  they  pass.  When  rotating  slowly, 
separate  puffs,  from  which  it  hardly 
seems  possible  to  construct  a  musical 
sound,  are  heard.  When,  however,  the 
ear  is  no  longer  able  to  detect  the  sepa- 
rate puffs,  the  sound  becomes  quite  musi- 
cal, and  the  pitch  rises  and  falls  with  the 
speed. 

Pitch  depends  upon  the  number  of  sound-waves  striking  the 


FIG.  169. 


208  MOLAR    DYNAMICS. 

ear  per  second.  If  the  source  of  the  sound-leaves  and  the  receiv- 
ing ear  be  both  stationary,  the  pitch  depends  upon  the  frequency 
of  vibration,  or  wave-length;  i.e.  the  greater  the  number  of 
vibrations  per  second,  or  the  shorter  the  ivave-length,  the  higher 
the  pitch. 

Since  pitch  depends  upon  the  number  of  sound-waves  strik- 
ing the  ear  per  second,  a  sound  must  rise  in  pitch  if  we 
rapidly  approach  the  source  of  the  sound-waves,  or  the  source 
rapidly  approach  us,  as  evidently  more  sound-waves  will  then 
strike  the  ear  per  second  than  otherwise  would  happen.  The 
pitch  of  the  whistle  rises  on  the  rapid  approach  of  a  locomo- 
tive, and  falls  again  as  the  engine  travels  away.1 


1  It  may  be  of  interest  to  consider  more  in  detail  two  cases  of  relative  motion 
between  the  ear  and  the  sounding  body  : 

Case  I.    Source  stationary  and  ear  approaching  it  with  velocity  i\  (Fig.  170)  per 


FIG.  170. 

second.  Let  v  =  the  velocity  of  the  sound-waves  per  second,  and  n  =  the  number  of 
vibrations  made  by  the  vibrating  body  (e.g.  a  fork)  per  second.  The  wave-length  is 

—  and  the  number  of  waves  in  the  space  r,  is  v,  -. —  or  — u  •  The  number  of  waves 
n  n  v 

striking  the  ear  per  second  is,  therefore,  n  +  — *— ,  or  n  ( 1  +  •  11.    If  i\  =  v,  the  tone 

v  '  V        v  ) 

perceived  is  an  octave  above  the  normal  pitch  of  the  fork.  If  vl  =  v,  but  the  motion 
of  the  ear  be  away  from  the  fork,  this  quantity  becomes  n  (1—1),  or  zero,  and  no 
sound-waves  reach  the  ear. 

Case  II.    Ear  stationary,  but  the  fork  moves  towards  it  with  a  velocity  of  r2  per 
second.    While  the  fork  moves  from  A  to  B  (Fig.  171),  the  first  sound-wave  sent  out 


FIG.  171. 

from  the  fork  at  the  beginning  of  the  second  has  travelled  all  the  way  from  A  to  C. 
The  last  wave  sent  out  in  that  second  of  time  is  just  starting  from  B  when  the  very 
first  wave  has  reached  C.  Thus  there  are  n  waves  between  B  and  C,  and  the  length 


VIBRATION-FREQUENCY    OF    A    TONE.  209 

174.  How  to  find  the  vibration-frequency  of  a  tone.  —  The 
siren.  —  The  perforated  wheel  described  above  is  a  cheap 
imitation  of  a  portion  of  an  important  instrument  called  a 
siren.  The  instrument  complete  has  an  attachment  called  a 
counter,  which  shows  the  number  of  revolutions  the  wheel 
makes  in  a  given  time. 

Suppose  that  it  is  required  to  ascertain  the  number  of 
vibrations  per  second  necessary  to  produce  a  given  pitch. 
Take  some  instrument  that  gives  the  required  pitch,  e.g.  a 
tuning-fork,  and  set  it  in  vibration ;  also  rotate  the  siren, 
causing  the  pitch  of  its  sound  gradually  to  rise  until  it  corre- 
sponds with  the  pitch  of  the  fork;  then,  sustaining  that 
pitch,  set  the  counter  in  operation,  and  at  the  end  of  a  given 
time  read  off  the  number  of  revolutions  made  by  the  wheel ; 
this  number  multiplied  by  the  number  of  holes  in  the  wheel 
gives  the  number  of  sound-waves  produced  by  the  wheel 
during  the  given  time,  and  the  number  of  vibrations  made  by 
the  fork  in  the  same  time ;  and  this  number  divided  by  the 
number  of  seconds  employed  gives  the  number  of  vibrations 
that  must  be  made  in  a  second  by  any  instrument  in  order  to 
produce  a  sound  of  the  same  pitch.  With  the  siren  we  may 
even  determine  the  number  of  vibrations  made  by  the  wing  of 
a  fly  which  buzzes  around  our  ears. 

The  vibration  frequency  of  a  fork  may  be  easily  found  by  means 
of  an  apparatus  called  a  vibrograph.  One  of  the  tines  of  the  fork  a 
(Fig.  172)  has  a  small  elastic  indicator  attached  to  its  extremity. 
The  sharp  point  of  this  indicator  touches  a  smoked  glass  plate,  fc, 
below.  Above  the  glass  plate  is  suspended  a  pendulum  with  a 
heavy  bob.  Beneath  the  bob  is  another  indicator  which  just  grazes 

of  each  is  only 2>  and  the  number  of  vibrations  received  by  the  ear  per  second  is 

v  -i- -*»  or This  shows  that  when  vz—  v,  this  fraction  has  the  value  oo ; 

?i  v  —  ^'2 

also  that  in  order  to  get  the  octave  above  the  normal,  v2  must  equal  |- 

It  is  obvious  that  in  Case  II.  there  is  a  shortening  of  the  waves,  but  there  is  no 
shortening  in  Case  I. 


210  MOLAK    DYNAMICS. 

the  glass  as  it  passes  the  lower  part  of  its  arc.  The  experimenter 
first  finds  the  exact  fraction  of  a  second  occupied  by  the  pendulum 
in  making  one  complete  or  double  vibration.  The  fork  is  then  put 
in  vibration  and  the  block  h  carrying  the  glass  plate  is  drawn  along 


beneath  the  style,  which  marks  upon  the  glass  a  wave  line.  Imme- 
diately after  the  glass  is  put  in  motion  the  pendulum  is  set  swinging 
and  allowed  to  traverse  the  plate  width-wise  three  times,  making, 
with  its  indicator,  three  lines  athwart  the  wave  line.  Now  the 
interval  of  time  between  the  instants  when  the  first  and  the  third 
of  these  lines  are  made  is  the  time  of  one  complete  vibration.  The 
number  of  vibrations  which  the  fork  made  in  this  interval  may  be 
determined  from  the  sinuous  curved  line  intervening  between  the 
lines  made  by  the  pendulum.  The  number  of  vibrations  made  by  the 
fork  in  a  certain  fraction  of  a  second  having  been  ascertained  in  this 
manner,  the  vibration  number  per  second  is  calculated  therefrom. 

175.  Distinction  between  noise  and  musical  sound.  —  If  the 
body  that  strikes  the  air  deal  it  but  a  single  blow,  like  the 
discharge  of  a  fire-cracker,  the  ear  receives  but  a  single  shock, 
and  the  result  is  called  a  noise.  If  several  shocks  be  slowly 
received  by  the  ear  in  succession,  the  ear  distinguishes  them 
as  so  many  separate  noises.  If,  however,  the  body  that  strikes 
the  air  be  in  vibration,  and  deal  it  a  great  number  of  little 
blows  in  a  second,  or  if  a  large  number  of  fire-crackers  be 


MUSICAL   SCALE.  211 

discharged  one  after  another  very  rapidly,  so  that  the  ear  is 
unable  to  distinguish  the  individual  shocks,  the  effect  produced 
is  that  of  one  continuous  sound,  which  may  be  pleasing  to  the 
ear ;  and,  if  so,  it  is  called  a  musical  sound.  But  continuity 
of  sound  does  not  necessarily  render  it  musical.  The  sound 
produced  by  a  hundred  children  beating  various  articles  in  a 
room  with  clubs  might  not  be  lacking  in  continuity,  but  it 
would  be  an  intolerable  noise.  There  would  be  wanting  those 
elements  that  please  the  ear ;  viz.  regularity  both  in  perio- 
dicity and  intensity  of  the  shocks  which  it  receives.  The 
distinction  between  music  and  noise  is,  generally  speaking, 
a  distinction  between  the  agreeable  and  the  disagreeable, 
between  regularity  and  confusion. 

176.    Musical  scale.  —  Suppose  a  body,  e.g.  a  tuning  fork, 
to  make  261  vibrations  per  second,  the  sound  produced  is 


recognized  by  our  musical  sense  as  the  note  gt—         -   which 


corresponds  with  the  so-called  middle  C  (cf,  or  French  ut3)  of 
a  piano  tuned  to  the  national  standard  pitch.1 

The  pitch  of  a  sound  produced  by  twice  as  many  vibrations 
as  that  of  another  sound  is  called  the  octave  of  the  latter. 
Between  two  such  sounds  the  voice  rises  or  falls,  in  a  manner 
very  pleasing  to  the  ear,  by  a  definite  number  of  steps  called 
musical  intervals.  This  gives  rise  to  the  so-called  diatonic 
scale,  or  gamut.  Long  before  any  one  had  attempted  to  find 
the  frequency  of  vibration  of  a  sounding  body,  men  had  used 
a  succession  of  sounds,  differing  in  pitch,  determined  only  by 
their  musical  sense  and  not  by  arbitrary  agreement.  The 
number  of  vibrations  which  shall  constitute  a  given  note  is 
purely  arbitrary,  and  differs  slightly  in  different  countries ; 

1  In  a  convention  of  piano  manufacturers  held  in  New  York  it  was  decided  that 
the  national  pitch  to  go  into  effect  July  1,  1892,  should  be  the  standard  French, 
Austrian,  and  Italian  pitch  of  435  (A3)  double  vibrations  in  a  second  at  68°  F. 


212  MOLAR    DYNAMICS. 

but  the  ratios  between  the  vibration  numbers  of  the  several 
notes  of  the  gamut  and  the  vibration  number  of  the  first  or 
fundamental  note  of  the  gamut,  are  the  same  among  all 
enlightened  nations. 

The  successive  tones  of  the  diatonic  scale  of  C  are  related 
to  one  another  with  .respect  to  vibr^ion  frequency  as  follows  : 

Q     *&f  '  jrft-    *$f  -4^- 

8= 


c' 

d' 

e' 

f 

g' 

a' 

b' 

No.  of  vi- 
brations 

261 

293.62 

326.25 

348 

so!3 
391.5 

435 

489.37 

Ratios 

256 

:     288 

:    320    : 

341.3 

:   384     : 

426 

:    480 

or 

1 

:        9 

:      |       : 

f 

:      ^       : 

9 

:       3jA 

c" 

ut4 
522 

512 
2 

The  ear  is  wholly  incapable  of  determining  the  number  of 
vibrations  corresponding  to  a  given  tone,  but  it  is  capable  of 
determining  with  wondrous  precision  the  ratio  of  the  vibration 
numbers  of  two  notes  ;  hence  all  music  must  depend  upon  the 
recognition  of  such  ratios,  and  for  this  reason  the  vibration 
ratios  given  above  are  of  the  utmost  importance.  An  octave 
below  c'  is  c ;  two  octaves  below,  c1?  and  so  on.  In  a  similar 
manner  the  octaves  below  any  other  tone  are  indicated. 

The  following  are  some  of  the  various  musical  intervals  occurring 
within  the  diatonic  scale  :  Minor  second,  e'  :  f  or  b'  :  c"  :  :  15  :  16  ; 
Major  second,  c'  :  <T,  f '  :  g',  or  a'  :  b'  :  :  8  :  9 ;  Minor  third,  e'  :  g'  or 
a'  :  c"  :  :  5  :  6  ;  Major  third,  c'  :  e',  f  :  a',  or  g'  :  b'  :  :  4  :  5  ;  fourth, 
c' :  f,  d' :  g7,  e' :  a',  or  g'  :  c"  :  :  3  :  4  ;  fifth,  c'  :  g7,  e'  :  b',  or  f  :  c"  :  : 
2:3,  etc. 

177.  Limits  of  scale  and  of  audibility.  —  The  lowest  note 
of  a  7-£  octave  piano  makes  about  27^  vibrations  per  second ; 
the  highest,  about  4,224  vibrations  per  second ;  but  these 
extreme  notes  have  little  musical  value,  and  the  lowest  notes 
are  chiefly  used  for  their  harmonics  only  (see  p.  220). 
The  range  of  the  human  voice  lies  between  61  and  1305 


LIMITS    OF    SCALE    AND    OF    AUDIBILITY.  213 

vibrations  per  second,1  or  a  little  more  than  three  octaves  ;  an 
ordinary  singer  has  about  the  compass  of  two  octaves. 

The  ear  is  capable  of  hearing  vibrations  far  exceeding  in 
number  the  requirements  of  music.  It  can  appreciate  sounds 
arising  from  32  to  38,000  vibrations2  per  second,  i.e.  a  range 
of  about  eleven  octaves,  and  a  corresponding  range  of  wave- 
length between  seventy  feet  and  three  or  four  tenths  of  an 
inch.  These  numbers  vary  considerably,  however,  with  the 
person.  Exceptional  ears  can  hear  as  many  as  50,000  vibra- 
tions. Some  ears  can  hear  a  bat's  cry,  or  the  creaking  of  a 
cricket;  others  cannot.  Singing  mice  are  sometimes  placed 
on  exhibition.  Of  those  who  go  to  hear  them,  some  can  hear 
nothing,  others  a  little,  and  others  again  can  hear  much.  In 
the  ability  to  hear  sharp  sounds,  no  animal  is  superior  to  the 
cat,  which  finds  her  prey  in  the  dark  by  its  squealing.  High 
tones  are  heard  with  difficulty  in  the  presence  of  low  ones. 
A  lower  tone  tends  to  drown  a  higher  one. 

Exercises. 

1.  Find  the  vibration  number  for  each  note  of  the  scale  of  which  of'  is 
the  first  note. 

2.  What  is  the  vibration  number  of  c  an  octave  below  c'  ? 

3.  Find  the  wave-length  corresponding  to  each  note  of  the  scale  of 
which  c'  is  the  first,  when  the  temperature  of  the  air  is  16°  C.  ? 

4.  Find  the  length  of  a  resonance  tube  (disregarding  its  diameter) 
closed  at  one  end,  which  will  respond  to  c"  when  the  temperature  is 
16°  C.  ? 

5.  a.  The  interval  between  e'  and  c"  is  called  a  minor  sixth ;  what  jjs 
the  vibration  ratio  for  this  interval  ?    b.  What  is  the  note  a  minor  sixth 
above  a'  ? 

6.  Make  out  a  series  of  fractions  which  shall  express  the  vibration 
ratios  of  each  tone  in  the  diatonic  scale  c",  d",  etc.,  as  compared  with 
c';   i.e.  continue  the  series  of  ratios  given  on  p.  212  through  another 
octave. 

1  Pietro  Blaserna,  in  his  "  Theory  of  Sound." 

2  Preyer  places  the  lowest  limit  for  some  ears  at  16  vibrations  per  second. 


214  MOLAR    DYNAMICS. 

7.  What  is  the  vibration  number  of  a'  in  a  scale  in  which  c'  (the  key- 
note) =  256  vibrations  ? 

8.  The  same  singer  may  not  be  able  to  sing  twice  alike,  i.e.  in  the 
same  key  ;  how  is  it  possible  that  the  singing  in  both  instances  may  be 
equally  correct  ? 

9.  If  one  ear  can  hear  a  certain  sound  at  5  feet  from  the  sounding 
body,  and  another  ear  at  only  3  feet,  how  many  times  more  sensitive  is 
the  former  ear  than  the  latter  ? 

10.  Why  does  the  same  bell  always  give  a  sound  of  nearly  the  same 
pitch  ? 

11.  a.  What  is  the  effect  of  striking  a  bell  with  different  degrees  of 
force  ?   6.  What  change  in  the  vibrations  is  produced  ?   c.  What  property 
of  sound  remains  the  same  ? 

12.  a.  Strike  a  key  of  a  piano  and  hold  it  down ;  what  is  the  only 
change  you  observe  in  the  sound  produced,  while  it  remains  audible  ? 
6.  What  is  the  cause  of  this  change  ? 

SECTION  VII. 

COMPOSITION  OF  SONOROUS  VIBRATIONS  AND  THEIR  RESULTANT 
WAVE-FORMS. 

178.  Coexistence  and  superposition  of  waves.  —  Interference. 
-  When  two  or  more  currents  of  waves  traverse  the  same 
medium  at  the  same  time  and  in  the  same  direction,  so  that 
one  set  of  waves  is,  as  it  were,  superposed  upon  another,  there 
are  imparted  to  every  particle  of  the  medium  simultaneously 
all  the  vibratory  motions  peculiar  to  the  several  waves.  When 
two  or  more  systems  of  waves  act  on  a  particle  at  the  same 
time,  they  are  said  to  interfere.  The  resultant  motion  of  any 
particle  at  a  given  instant  would  be  found  on  the  principle  of 
parallelogram  of  motions ;  or,  in  case  the  several  motions  are 
parallel  and  occur  in  the  same  time,  the  resultant  is  the 
algebraic  sum  of  the  several  motions.  This  will  be  best 
understood  by  means  of  graphical  representations.  In  A 
(Fig.  173)  are  represented  by  dotted  lines  the  wave  lines  of 
two  coexisting  currents  of  waves  having  the  same  wave-length 


COEXISTENCE    AND    SUPERPOSITION    OF    WAVES.     215 

and  phase,  but  the  amplitude  of  one  greater  than  that  of  the 
other.     For  example,  the  amplitudes  of  the  vibrations  for  the 
particle  a  are  respectively  a  c 
and  a  e.    Their  algebraic  sum 
is  ad.     In  like  manner  the 
displacement  of  any  particle 
of  the  medium  traversed  by 
the  several  wave  currents  at 
any  instant  is  determined. 
The   heavy  line   represents    Q_ 
the  form  of  the  joint  wave 
resulting  from  the  combina- 
tion of  the  two.     It  will  be 
seen  that  the  only  change  is          /—^     ^     /-" 

one  of  amplitude  or  inten-       c^ ^^___^\^-     ^C   —^ 

^—~-'   \        /  v-__-'x  \ 
sity. 

In   B   are  two   wave-cur- 
rents  whose  waves   are   of 

the  same  length  and  ampli-  \/      \/      \/      \ 

tude,  but  with  a  difference  A  y\ 

of  phase  of  i  of  a  period. 

FIG.  173. 
i.e.   one    is   a   quarter  01  a 

wave-length  behind  the  other.  The  result  is  a  wave  of  the 
same  length,  but  of  different  phase  and  amplitude. 

In  C  are  two  sets  of  waves  of  like  length,  of  different 
amplitudes,  and  of  opposite  phases,  or  one  is  half  a  wave- 
length behind  the  other.  The  result  is  a  set  of  waves  of  the 
same  length,  but  diminished  intensity.  In  D  the  conditions 
are  the  same  as  in  C  except  that  the  components  have  the 
same  amplitude.  The  result  is  that  the  two  components  de- 
stroy each  other,  and  the  particles  of  the  medium  are  undis- 
turbed, as  indicated  by  the  straight  line. 

In  A  (Fig.  174)  are  given  two  wave-currents  whose  wave- 
lengths are  as  1  :  %  and  whose  phases  in  the  beginning  agree. 


216 


MOLAR    DYNAMICS. 


The  resultant  of  this  combination  with  still  another  of  ^  the 
wave-length  of  the  longest  is  shown  in  B.     In  C  is  the  same 


FIG.  174. 


combination  as  in  A,  but  the  phases  differ  by  £  of  a  period  of 
the  shorter  wave. 

Fig.  175  represents  wave-lines  drawn  by  a  vibroyrapli.    The 
second  line  represents  a  sound  two  octaves  above  that  which 


2  'NA/V\AAAAAAA/W\AA/WWVW\A/W\A^ 


FIG.  175. 

the  first  line  represents,  and  the  third  line  shows  the  result 
that  is  produced  by  causing  the  fork  to  have  two  sets  of 
simultaneous  vibrations. 

Extend  the  arm  horizontally  and  cause  the  hand  to  move  from 
side  to  side  through  a  wide  arc  and  at  the  same  time  cause  the 


COEXISTENCE   AND    SUPERPOSITION    OF    WAVES.     217 


hand  to  move  in  the  same  plane  through  shorter  arcs  in  a  sort  of 
jerky  movement.  The  result  of  these  combined  motions  bears  some 
faint  resemblance  to  the  motion  of  the  tine  as  it  draws  line  3  above, 
or  to  the  motion  of  an  air  particle  as  the  two  currents  of  waves 
generated  by  the  fork  pass  it. 

One  may  see  a  typical  representation  of  superposed  waves,  or 
currents  of  small  waves  and  wavelets  creeping  over  the  backs  of 
larger  ones  and  carving  their  surfaces  into  ragged  and  ever-changing 
outlines,  in  watching  the  billows  of  the  sea,  especially  when  the 
surface  is  swept  by  a  breeze  of  varying  intensity. 

In  the  diagrams  given  above  only  transverse  vibrations  are 
represented,  but  the  results  there  depicted  apply  equally  well 
to  longitudinal  vibrations  and  waves  of  condensations  and 
rarefactions.  In  Fig.  176  the  heavy  line  AB  is  a  typical 
representation  of  the  resultant  of  two  currents  of  aerial 

ct 


FIG.  176. 


sound-waves  an  octave  apart,  while  the  rectangular  diagram 
C  D  is  intended  to  represent  a  portion  of  a  transverse  section 
of  a  body  of  air  traversed  by  the  joint  wave  corresponding  to 
the  heavy  wave-line  above.  The  depth  of  shading  in  different 
parts  indicates  the  degree  of  condensation  or  rarefaction  at 
those  parts. 


218  MOLAR   DYNAMICS. 


SECTION  VIII. 

VIBRATION    OF    STRINGS. 

179.  Sonometer.  —  This  instrument  consists  of  two  or  more 
piano-wires  of  different  thicknesses  stretched  lengthwise  over 
a  resonance  box.  One  end  of  each  wire  is  attached  to  the 
shorter  arm  of  a  bent  lever,  A  or  B  (Fig.  177),  and  the  tension 


FIG.  177. 

of  the  wire  is  regulated  both  by  the  lengths  of  the  longer 
arms  employed  and  by  the  magnitude  of  the  weights  suspended 
therefrom.  The  length  of  the  vibrating  portion  of  the  strings 
is  regulated  by  the  sliding  bridge  C. 

Experiment  1.  —  Remove  the  bridge  C,  pluck  one  of  the  strings  with 
the  fingers  at  the  middle  point,  causing  it  to  vibrate  as  a  whole,  and  note 
the  pitch  of  the  sound.  Place  the  bridge  under  the  same  wire,  and  move 
it  gradually  toward  one  end  of  the  sonometer,  thereby  shortening  the 
vibrating  portion ;  the  pitch  rises  as  the  vibrating  portion  is  shortened. 
Vary  the  position  of  C  until  a  pitch  is  obtained  an  octave  above  the  pitch 
given  at  first  when  the  entire  wire  was  vibrating.  It  will  be  found  that 
the  length  of  the  wire  which  gives  the  higher  note  is  just  half  the  original 
length ;  i.  e.  by  halving  the  wire  its  vibration-number  is  doubled.  At  two- 
thirds  its  original  length,  it  gives  a  note  at  an  interval  of  a  fifth  above 
that  given  by  its  original  length ;  and  generally  the  reciprocals  of  the 
fractions  (p.  212)  representing  the  relative  vibration-numbers  of  the 
several  notes  of  a  scale  represent  the  relative  lengths  of  the  wires  that 
produce  these  notes. 

Now  increase  the  tension  of  the  wire ;  the  pitch  rises.  Increase  the 
tension  until  the  pitch  has  risen  an  octave;  it  will  be  found  that  the 
tension  has  been  increased  fourfold. 


STATIONARY    VIBRATIONS,    NODES,    ETC.  219 

Next  try  two  wires  whose  lengths  and  tension  are  the  same,  but  whose 
diameters  are  (say)  as  1  :  2,  and  whose  masses  are  consequently  as  1  : 4  ; 
the  pitch  given  by  the  wire  of  greater  mass  is  an  octave  lower  than  the 
pitch  given  by  the  other  wire. 

These  conclusions  may  be  summarized  thus  :  The  vibration- 
numbers  of  strings  of  the  same  material  vary  inversely  as  their 
lengths  and  the  square  roots  of  their  masses  per  unit  length,  and 
directly  as  the  square  roots  of  their  tensions. 

180.    Stationary  vibrations,  nodes,  etc. 

Experiment  2.  —  Hold  one  end  of  a  rubber  tube  about  2  m  long,  while 
the  other  is  fixed,  and  send  along  it  a  regular  succession  of  equal  pulses 
from  the  vibrating  hand ;  it  will  be  easy,  by  varying  the  tension  a  little, 
to  obtain  a  succes- 
sion  of  gauzy  spindles 
(Fig.  178)  separated 
by  points  that  are 
nearly  or  quite  at  rest. 

Unlike  the  earlier  experiments,  the  waves  here  do  not  appear  to  travel 
along  the  tube ;  yet  in  reality  they  do  traverse  it.  The  deception  is 
caused  by  stationary  points  being  produced  by  the  interference  of  the 
advancing  and  retreating  waves. 

This  interference  of  direct  and  reflected  waves  gives  rise 
to  an  important  class  of  phenomena  called  stationary  vibra- 
tions. The  points  of  least  motion,  as  a,  b,  and  e  (Fig.  178),  are 
called  nodes  (from  fancied  resemblance  to  knots) ;  the  points 
of  greatest  amplitude,  as  d  and  <?,  are  called  antinodes;  and  the 
portions  between  the  nodes  are  called  venters. 

In  a  similar  manner  a  string  may  be  made,  to  vibrate  in  3, 
4,  etc.,  parts,  as  shown  in  C,  D^-and  E  (Fig.  179).  The  pitch 
of  the  tone  produced  by  a  string  when  it  vibrates  as  a  whole, 
as  in  A,  is  called  the  fundamental  pitch  of  the  string.  The 
vibration  frequency  when  the  string  divides  into  halves,  as 
in  B,  is  twice  as  great  and  consequently  the  pitch  of  the  tone 
produced  is  an  octave  above  that  of  the  fundamental.  Gen- 
erally the  vibration  frequency  varies  as  the  number  of  venters 
into  which  the  string  divides. 


220 


MOLAR    DYNAMICS. 


Tones  produced  by  a  string  or  other  body  that  vibrates  in 
parts  are  called  overtones  or  partial  tones.     If  the  overtones 


FIG.  179. 

harmonize   (p.  223)   with  the  fundamental  of  the  vibrating 
body,  they  are  called  harmonics. 
181.    Complex  vibrations. 

Experiment  3.  —  Strike  one  of  the  lowest  notes  of  a  piano,  hold  the 
key  down,  and  immediately  apply  the  tip  of  the  finger  to  some  point  of 
the  wire  struck,  and  notice  any  changes  in  tone  that  may  occur  after 
applying  the  linger.  Repeat  this  at  many  points  along  the  string.  If  the 
fundamental  sound  disappear,  there  will  probably  be  a  sound  of  a  higher 
pitch  that  will  continue,  showing  that  although  you  have  stopped  one  set 
of  vibrations,  there  were  still  other  vibrations  in  the  string  of  a  higher 
vibration-period  which  you  did  not  stop,  and  which  now  become  audible 
since  the  louder  fundamental  is  silenced. 

Experiment  4.  —  Press  down  the  C'-key  gently,  so  that  it  will  not 
sound ;  and  while  holding  it  down,  strike  the  C-key  strongly.  In  a  few 
seconds  release  the  key,  so  that  its  damper  will  stop  the  vibrations  of  the 
string  that  was  struck,  and  you  will  hear  a  sound  which  you  will  recog- 
nize by  its  pitch  as  coming  from  the  C'-wire.  Place  your  finger  lightly  on 
the  C'-wire,  and  you  will  find  that  it  is  indeed  vibrating.  Press  down  the 
right  pedal  with  the  foot,  so  as  to  lift  the  dampers  from  all  the  wires, 
strike  the  C-key,  and  touch  with  the  finger  the  C'-wire;  it  vibrates. 
Touch  the  wires  next  to  C',  viz.  B  and  D' ;  they  have  only  a  slight  forced 
vibration.  Touch  G' ;  it  vibrates. 

Now  it  is  evident  that  the  vibrations  of  the  C'  and  G'-wires 
are  sympathetic.  But  a  C-wire  vibrating  as  a  whole  cannot 
cause  sympathetic  vibrations  in  a  C'-wire  ;  but,  if  it  vibrates 


TONES    AND    NOTES.  221 

in  halves,  it  may.  .  Hence,  we  conclude  that  when  the  C-wire 
was  struck  it  vibrated,  not  only  as  a  whole,  giving  a  sound  of 
its  own  pitch,  but  also  in  halves  ;  and  the  result  of  this  latter 
set  of  vibrations  was,  that  an  additional  sound  was  produced 
by  this  wire,  just  an  octave  higher  than  the  first-mentioned 
sound. 

Again,  the  G'-wire  makes  391.5  vibrations  in  a  second,  or 
three  times  as  many  (130.5)  as  are  made  by  the  C-wire  ;  hence 
the  latter  wire,  in  addition  to  its  vibrations  as  a  whole  and  in 
halves,  must  have  vibrated  in  thirds,  inasmuch  as  it  caused 
the  G'-wire  to  vibrate.  It  thus  appears  that  a  string  may 
vibrate  at  the  same  time  as  a  whole,  in  halves,  thirds,  etc., 
and  the  result  is  that  a  sensation  is  produced  that  is  com- 
pounded of  the  sensations  of  several  sounds  of  different  pitch. 
A  sound  so  simple  that  it  cannot  be  resolved  (see  p.  227)  is 
called  a  tone, 

182.  Tones  and  notes.  —  A  sound  composed  of  many  tones 
is  called  a  note. 

Not  only  do  stringed  instruments  produce  notes,  but  110 
ordinary  musical  instrument  is  capable  of  producing  a  simple 
tone,  i.e.  a  sound  generated  by  vibrations  of  a  single  period. 
In  other  words,  when  any  note  of  any  musical  instrument  is 
sounded,  there  is  produced,  in  addition  to  the  primary  tone,  a 
number  of  other  tones  in  a  progressive  series,  each  tone  of  the 
series  being  usually  of  less  intensity  than  the  preceding}-  The 
primary  or  lowest  tone  of  a  note  is  usually  sufficiently  intense 
to  be  the  most  prominent,  and  hence  is  called  the  fundamental 
tone. 

Strings  when  struck  produce  many  overtones,  according  to 
the  place  where  they  are  struck,  the  nature  of  the  stroke,  and 
the  density,  rigidity,  and  elasticity  of  the  string. 

1  The  so-called  Fourier  theorem  translated  from  the  language  of  kinematics  into 
that  of  acoustics  asserts  that  "  every  regular  musical  sound  is  resolvable  into  a 
definite  number  of  simple  tones  whose  relative  pitch  follows  the  law  of  the  partial- 
tone  series." 


222 


MOLAR   DYNAMICS. 


183.    Beats. 


Experiment  5.  —  Strike  simultaneously  the  lowest  note  of  a  piano  and 
its  sharp  (black  key  next  above),  and  listen  to  the  resulting  sound. 

You  hear  a  peculiar  wavy  or  throbbing  sound,  caused  by  an 
alternate  rising  and  sinking  in  loudness.  This  phenomenon 
is  still  more  conspicuous  where  the  two  lowest  adjacent  notes 
of  a  large  organ  are  sounded  together.  Each  recurrence  of 
the  maximum  intensity  is  called  a  beat. 

Let  the  continuous  curved  line  A  C  (Fig.  180)  represent  a 
series  of  waves  caused  by  striking  the  lower  key,  and  the 


FIG.  189. 

dotted  line  a  series  of  waves  proceeding  from  the  upper  key. 
Now  the  waves  from  both  keys  may  start  together  at  A  ;  but 
as  the  waves  from  the  lower  key  are  given  less  frequently,  so 
are  they  correspondingly  longer  ;  and  at  certain  intervals,  as 
at  B,  condensations  will  correspond  with  rarefactions,  pro- 
ducing by  their  interference  momentary  silence,  too  short, 
however,  to  be  perceived  ;  but  the  sound  as  perceived  by  the 
ear  is  correctly  represented  in  its  varying  loudness  by  the 
curved  line  A'B'C'. 

It  will  be  apparent  from  the  study  of  Fig.  180  that  exactly 
one  beat  will  occur  in  each  interval  of  time  during  which  the 
acuter  of  two  simple  tones  performs  one  more  vibration  than 
the  graver  tone. 

Hence  the  number  of  beats  per  second  due  to  tivo  simple  tones 
is  equal  to  the  difference  of  their  respective  vibration  numbers. 


ORIGIN   OF    HARMONY    AND   DISCORD.  223 

The  sensation  produced  011  the  ear  by  such  a*  throbbing  sound, 
when  the  beats  are  sufficiently  frequent,  is  unpleasant,  much 
as  the  sensation  produced  by  flashes  of  light  that  enter  the 
eye  when  you  walk  on  the  shady  side  of  a  picket  fence  is 
unpleasant.  The  unpleasant  sensation  called  by  musicians 
discord  is  due  to  beats. 

184.  Origin  of  harmony  and  discord.  —  The  harmonics  in 
any  note  are  produced  successively  by  two,  three,  etc.,  times 
the  number  of  vibrations  made  by  its  fundamental.  Hence, 
if  any  two  notes  an  octave  apart,  —  for  instance,  C  and  Cf,  — 
be  sounded  simultaneously,  there  will  result  for 

C,  1,  2,  3,  4,  5,  6,  etc.  >  j. 
*  A     t     f times  tne  number  of  vibrations  made 

by  the  fundamental  of  C  ;  so  that  the  fundamental  of  C',  and 
its  overtones  (with  the  exception  of  the  highest  overtones, 
which  are  too  feeble  to  affect  the  general  result),  are  in  perfect 
unison  with  the  overtones  of  C.  Not  only  is  there  perfect 
agreement  among  the  overtones  of  two  notes  an  octave  apart 
when  sounded  together,  as  when  male  and  female  voices  unite 
in  singing  the  same  part  of  a  melody,  but  the  richness  and 
vivacity  of  the  sound  are  much  increased  thereby. 

Discord  produced  by  two  sounds  is  explained  by  the  fact 
that  the  sounds  produce  beats,  which  do  not  coalesce  because 
the  interval  between  them  is  too  long. 

As  the  frequency  of  the  beats  increases,  a  point  is  finally 
reached  where  they  cease  to  be  recognized  as  distinct 
sounds  and  where  they  blend  into  a  more  or  less  pure 
tone.  Beats  may  thus  coalesce  to  produce  beat-tones  that 
are  musical. 

It  must  not,  however,  be  inferred  that  dissonance  disap- 
pears immediately  upon  the  intermittences  becoming  too  rapid 
for  individual  recognition.  If  two  tones  form  a  narrower 
interval  than  a  minor  third,  the  combined  sound  is  harsh  and 
grating  on  the  ear. 


224  MOLAR    DYNAMICS. 

Two  tones  must  be  in  unison  to  produce  absolutely  perfect 
harmony.  The  nearest  approach  to  it  is  an  interval  of  an 
octave,  and  next  in  rank  to  the  latter  is  a  fifth. 

That  two  notes  sounded  together  may  harmonize,  it  is  essential 
not  only  that  the  pitch  of  their  fundamental  tones  be  so  widely 
different  that  they  cannot  produce  audible  beats,  but  that  no 
audible  beats  shall  be  formed  by  their  overtones,  or  by  an  over- 
tone and  a  fundamental. 

For  example,  let  the  vibration-numbers  of  the  fundamentals 
of  C'  and  its  octave  C"  be  respectively  264  and  528  ;  the  num- 
ber of  beats  that  they  give  is  264  in  a  second.  If,  instead  of 
C",  a  note  the  vibration-number  of  whose  fundamental  is  527 
be  sounded  with  C,  the  number  of  beats  produced  by  their 
fundamentals  would  be  263,  and  no  discord  would  result 
therefrom  ;  but  there  would  be  one  beat  per  second  between 
the  first  overtone  of  C'  and  the  fundamental  of  C",  and  this 
would  introduce  a  discord. 

Observe  that  the  relation  between  the  vibration-numbers  of 
the  fundamentals  of  C  and  C',  C  and  G,  C  and  F,  and  C  of 
any  diatonic  scale  and  any  note  in  the  same  scale,  can  be 
expressed  in  terms  of  small  numbers,  e.g.  1:2,  2  :  3,  3  :  4, 
etc.  (see  p.  212).  Generally,  those  notes  and  only  those  har- 
monize whose  fundamental  tones  bear  to  one  another  ratios 
*  expressed  by  small  numbers;  and  the  smaller  the  numbers  which 
express  the  ratios  of  the  rates  of  vibration,  the  more  perfect  is 
the  harmony  of  two  sounds. 

Not  only  may  two  notes  whose  relative  vibration  frequency 
is  expressible  by  a  simple  ratio  harmonize,  but  three  or  four 
may  concur  with  the  same  result.  A  sound  produced  by  the 
coexistence  of  three  or  more  notes  is  called  in  music  a  chord. 
A  consonant  chord  is  a  concord ;  a  dissonant  chord  is  a  discord. 

Fig.  181  is  a  graphical  representation  according  to  Helmholtz  of 
the  amount  of  dissonance  contained  in  the  several  intervals  of  the 
diatonic  scale.  The  intervals  reckoned  from  C,  are  denoted  by  dis- 


ORIGIN    OF    HARMONY    AND    DISCORD.  225 

tances  measured  along  the  horizontal  straight  line.  The  dissonance 
for  each  interval  is  represented  by  the  vertical  distance  of  the  curved 
line  from  the  corresponding  point  on  the  horizontal  line.  If  we 
regard  the  outline  as  that  of  a  mountain  chain,  the  discords  would 


C  D  Efr   E  F  G         A6    A        Bb       B         C' 

FIG.  181. 

be  represented  by  peaks,  and  the  concords  by  passes,  while  the 
steepness  indicates  the  sharpness  of  definition  of  the  interval.  The 
calculations  on  which  the  curve  is  based  are  made  from  the  notes 
produced  by  a  violin.  For  piano-forte  notes  the  curve  would  be 
slightly  different. 

It  follows,  from  what  has  been  said,  that  only  a  limited 
number  of  notes  can  be  sounded  with  any  given  note  assumed 
as  a  prime  without  generating  discord.  Hence,  the  musical 
scale  is  limited  to  certain  determinate  degrees,  represented 
by  the  eight  notes  of  the  so-called  musical  or  diatonic  scale. 
This  scale  is  not  the  result  of  any  arbitrary  or  fanciful 
arrangement,  but  is  composed  of  notes  selected  because  they 
harmonize  with  the  prime  of  the  scale,  both  as  regards  their 
fundamental  tones  and  their  overtones. 


Exercises. 

1.  Prepare  a  table  of  the  series  of  overtones  of  C  and  G  respec- 
tively, as  on  p.  212,  and  ascertain  what  overtones  of  the  two  series  are  in 
unison. 

2.  Arrange  the  notes  in  a  single  octave  of  the  diatonic  scale  in  the 
order  of  their  rank  with  reference  to  their  harmonizing  with  the  prime 
of  the  scale,  on  the  principle  that  "the  smaller  the  numbers  which  ex- 


226  MOLAR   DYNAMICS. 

press  the  ratios  of  vibration,  the  more  perfect  is  the  harmony  of  two 
sounds." 

3.  Verify  your  conclusions  as  follows :  Strike  the  C-key  of  a  piano, 
together  with  each  of  the  seven  white  keys  above  it,  consecutively,  and 
compare  the  results  of  the  different  pairs  with  reference  to  harmony. 


SECTION  IX. 

QUALITY    OF    SOUND. 

185.  Simple  sound-waves  can  differ  only  in  length  and 
amplitude;  consequently  the  sounds  which  they  produce  can 
differ  only  in  pitch  and  loudness.  Complex  sound-waves  may 
differ,  as  we  have  seen,  in  /erm,  and  this  gives  rise  to  a  prop- 
erty of  sound  called  .quality  (by  musicians,  timbre).  Quality 
is  that  property  of  sound,  ,not  due  to  pitch  or  intensity,  that 
enables  us  to  distinguish  one  sound  from  another. 

Although  the  variety  of  sounds  one  hears  appears  well-nigh 
infinite,  yet  no  two  sounds  can  differ  from  each  other  in  any 
other  respect  than  pitch,  loudness,  or  quality.  The  length, 
amplitude,  and  form  of  the  wave  completely  determine  the 
wave,  and  these  three  elements  of  a  wave  are  mutually  inde- 
pendent, i.e.  any  one  may  be  changed  without  altering  the 
other  two.  Loudness  depends  on  amplitude  of  vibrations,  _ 
pitch  on  vibration-frequency,  and  quality  on  complexity  of 
the  motion  of  the  vibrating  particles. 

Let  the  same  note  be  sounded  with  the  same  intensity, 
successively,  on  a  variety  of  musical  instruments,  e.g.  a  violin, 
cornet,  clarinet,  accordion,  jews-harp,  etc.  ;  each  instrument 
will  send  to  your  ear  the  same  number  of  waves,  and  the 
waves  from  each  will  strike  the  ear  with  the -same  force,  yet 
the  ear  is  able  to  distinguish  a  decided  difference  between  the 
sounds,  —  a  difference  that  enables  us  instantly  to  identify 
the  instruments  from  which  they  come.  Sounds  from  instru- 
ments of  the  same  kind,  but  by  different  makers,  usually 


ANALYSIS    OF    SOUND-WAVES. 


227 


exhibit  decided  differences  of  character.  For  instance,  of  two 
pianos,  the  sound  of  one  will  be  described  as  richer  and  fuller, 
or  more  ringing,  or  more  "wiry,"  etc.,  than  the  other.  No 
two  human  voices  sound  exactly  alike. 


SECTION  X. 

ANALYSIS    AND    SYNTHESIS    OF    SOUND-WAVES. 

186.  Analysis  of  sound-waves.  —  The  unaided  ear  is  unable, 
except  to  a  very  limited  extent,  to  distinguish  the  individual 
tones  that  compose  a  note.  Helmholtz  arranged  a  series  of 
resonators  of  brass  nearly 
spherical  in  shape,  each  hav- 
ing two  openings;  one,  A 
(Fig.  182),  large,  for  the  re- 
ception of  the  sound-waves, 
and  the  other,  B,  small  and 
funnel-shaped,  and  adapted 
for  insertion  into  the  ear. 
Each  resonator  of  the  series 
was  adapted  by  its  size  to 
resound  powerfully  to  only  a 
single  tone  of  a  definite  pitch.  When  any  musical  sound  is 
produced  in  front  of  these  resonators,  the  ear,  placed  at  the 
orifice  of  any  one,  is  able  to  single  out,  from  the  total  number 
of  tones  composing  the  note,  that  overtone,  if  present,  to 
which  alone  this  resonator  is  capable  of  responding.  By 
applying  one  resonator  after  another  to  the  ear  a  sound  is 
analyzed  into  its  components.  It  is  thus  found,  for  instance, 
that  the  notes  of  a  clarinet  are  composed  only  of  the  odd 
harmonics,  or  of  tones  whose  vibration  numbers  are  in  the 
ratios  of  1  :  3  :  5  :  7 ;  and  that  the  notes  of  a  flute  are  substan- 
tially those  of  a  tone  and  its  octave.  It  is  found  that  when  a 


228  MOLAR    DYNAMICS. 

note  is  produced  on  a  given  instrument,  not  only  is  there  a 
great  variety  of  intensity  represented  by  the  overtones,  but 
all  the  possible  overtones  of  the  series  are  by  no  means 
present.  Which  are  wanting  depends  very  much,  in  stringed 
instruments,  upon  the  point  of  the  string  struck:  For  example, 
if  a  string  be  struck  at  its  middle  point,  no  node  can  be  formed 
at  that  point;  consequently,  the  two  important  overtones 
produced  by  2  and  4  times  the  number  of  vibrations  of  the 
fundamental  will  be  wanting.  Strings  of  pianos,  violins,  etc., 
are  generally  struck  near  one  of  their  ends,  and  thus  they  are 
deprived  of  only  some  of  their  higher  and  feebler  overtones. 

"  Every  vowel  is  a  particular  quality  of  sound."  The 
mouth  cavity  acts  as  a  resonator  and  reflector.  To  each 
vowel  corresponds  a  different  form  of  resonating  mouth  cavity. 
Upon  the  number  of  upper  overtones  which  are  reinforced, 
and  the  relative  intensities  of  the  reinforcement,  depends  the 
.quality  of  the  vowel  sound  produced.  Vowel  sounds  may  be 
analyzed  in  a  very  interesting  manner,  as  follows :  Raise  the 
cover  of  a  grand  piano,  press  down  the  "  loud  pedal,"  and 
sing  strongly  some  vowel  sound,  projecting  the  voice  upon 
the  exposed  strings.  When  you  cease  to  sing,  that  vowel  will 
be  repeated  by  the  strings.  Each  component  of  the  complex 
vibration  will  be  taken  up  by  that  string  in  unison  with  it, 
and  by  noticing  which  strings  vibrate  a  qualitative  analysis  of 
the  sound  is  effected. 

187.  Manometric  flames. — The  pitch,  intensity,  and  qual- 
ity of  a  sound  may  be  studied  at  the  same  time  by  causing 
sound-waves  to  impinge  directly  upon  some  sensitive  body 
without  any  intermediate  process  of  selection.  Apparatus 
like  that  shown  in  Fig.  183  will  serve  to  illustrate.  ' 

The  cylindrical  box  A  is  divided  by  the  membrane  a  into 
two  compartments,  c  and  b.  Illuminating-gas  is  introduced 
into  the  compartment  c,  through  the  rubber  tube  n,  and  burned 
at  the  orifice  d.  CD  is  a  frame  holding  two  mirrors,  M, 


MANOMETRIC    FLAMES. 


229 


placed  back  to  back,  so  that  whichever  side  is  turned  toward 
the  flame  there  is  a  reflection  of  the  flame. 

When  the  mirror  is  at  rest,  an  image  of  the  flame  will 
appear  in  the  mirror  as  represented  by  A  (Fig.  184).  If  the 
mirror  be  rotated,  the  flame  appears  drawn  out  in  a  band  of 
light,  as  shown  in  B  of  the  same  figure. 


FIG.  183. 

Sing  into  the  cone  B  (Fig.  183)  the  sound  of  oo  in  tool,  and 
waves  of  air  will  run  down  the  tube  and  beat  against  the 
membrane  a,  causing  it  to  vibrate.  The  membrane  has  im- 
pressed upon  it  a  complex  motion  resembling  the  original 
compound  vibration  of  the  vocal  chords  or  other  sounding 
body.  The  membrane  in  turn  acts  upon  the  gas  in  the  com- 
partment 6',  throwing  it  into  vibration. 


230 


MOLAR   DYNAMICS. 


The  result  is,  that  instead  of  a  flame  appearing  in  the  rotat- 
ing mirror  as  a  continuous  band  of  light,  as  B  -(Fig.  184),  it  is 
divided  up  into  a  series  of  tongues  of  light,  as  shown  in  C, 


U        -,f      .-.-.-.    =|JS§^-     -'       4:      -=£-^-     -JES3j_--^;=}f§5af         ^=JFS3,— _    ^^  SSf  ._    -_^_^    ==;-^_— _ 


FIG.  184. 


each  condensation  being  represented  by  a  tongue,  and  each 
rarefaction  by  a  dark  interval  between  the  tongues.  The 
number  and  size  of  the  greater  tongues  indicate  the  fre- 
quency and  amplitude  of  the  fundamental  vibration ;  the 


THE  PHONAUTOGRAPH  OR  PHONOGRAPH. 


231 


subsidiary  serrations  correspond  to  the  subsidiary  vibrations 
or  overtones. 

If  a  note  an  octave  higher  than  the  last  be  sung,  we  obtain, 
as  we  should  expect,  twice  as  many  tongues  in  the  same 
space,  as  shown  in  D.  E  represents  the  result  when  the  two 
tones  are  produced  simultaneously,  and  illustrates  in  a  strik- 
ing manner  the  effect  of  interference.  F  represents  the  result 
when  the  vowel  e  is  sung  at  the  pitch  of  C' ;  and  G-,  when 


FIG.  185. 

the  vowel  o  is  sung  on  the  same  key.  These  are  called  mano- 
metric  /lames. 

188.  The  phonautograph  or  phonograph.  —  Sound-waves, 
however  complex,  may  be  caused  permanently  to  record  the 
succession  and  variation  of  their  impulses,  and  thus,  as  it 
were,  to  inscribe  their  own  autograph.  Fig.  185  represents 
the  original  Edison  phonograph. 

A  metallic  cylinder  A  is  rotated  by  means  of  a  crank.  On 
the  surface  of  the  cylinder  is  cut  a  shallow  helical  groove 


232  MOLAR    DYNAMICS. 

running  around  the  cylinder  from  end  to  end,  like  the  thread 
of  a  screw.  A  small  metallic  point,  or  style,  projecting  from 
the  under  side  of  a  thin  metallic  disk  D  (Fig.  186)  which 

closes  one  orifice  of  the  mouth- 
piece B,  stands  directly  over  the 
thread.  By  a  simple  device  the 
cylinder,  when  the  crank  is  turned, 
is  made  to  advance  just  rapidly 
enough  to  allow  the  groove  to 

keep  constantly  under  the  style.  The  cylinder  is  covered 
with  tinfoil.  The  cone  F  is  usually  applied  to  the  mouth- 
piece to  concentrate  the  sound-waves  upon  the  disk  D. 

Now,  when  a  person  directs  his  voice  toward  the  mouth- 
piece, the  aerial  waves  cause  the  disk  D  to  participate  in 
every  motion  made  by  the  particles  of  air  as  they  beat  against 
it,  and  the  motion  of  the  disk  is  communicated  by  the  style 
to  the  tinfoil,  producing  thereon  impressions  or  indentations 
as  it  passes  on  the  rotating  cylinder.  The  result  is  that 
there  is  left  upon  the  foil  an  exact  representation  of  every 
movement  made  by  the  style.  Some  of  the  indentations  are 
quite  perceptible  to  the  naked  eye,  while  others  are  visible 
only  with  the  aid  of  a  microscope  of  high  power.  Fig.  187 
represents  a  piece  of  the  foil  as  it  would 
appear  inverted  after  the  indentations  (here 
greatly  exaggerated)  have  been  imprinted 
upon  it. 

The  words  addressed  to  the  phonograph  having  been  thus 
impressed  upon  the  foil,  the  mouth-piece  and  style  are  tem- 
porarily removed,  while  the  cylinder  is  brought  back  to  the 
position  it  had  when  the  talking  began,  and  then  the  mouth- 
piece is  replaced.  Now,  evidently,  if  the  crank  be  turned  in 
the  same  direction  as  before,  the  style,  resting  upon  the  foil 
beneath,  will  be  made  to  play  up  and  down  as  it  passes  over 
ridges  and  sinks  into  depressions  ;  this  will  cause  the  disk  D 


SYNTHESIS   OP   SOUND-WAVES.  233 

to  reproduce  the  same  vibratory  movements  that  caused  the 
ridges  and  depressions  in  the  foil.  The  vibrations  of  the 
disk  are  communicated  to  the  air,  and  through  the  air  to  the 
ear  ;  thus  the  words  spoken  to  the  apparatus  may  be,  as  it 
were,  shaken  out  into  the  air  again  at  any  subsequent  time, 
even  centuries  after,  accompanied  by  the  exact  accents,  into- 
nations, and  quality  of  sound  of  the  original. 

Subsequently  Edison  improved  this  instrument  by  replacing  the 
metallic  foil  by  a  cylinder  of  hard  wax  composition,  rotating  it  by 
an  electric  motor,  and  providing  an  improved  form  of  style  which 
engraves  upon  the  wax  the  most  delicate  variations  of  vibratory 
motions,  and  thus,  as  it  were,  reproduces  speech  and  musical  notes 
with  all  their  delicate  shades  of  expression  and  modulation.  In  its 
improved  form  it  has  become  a  commercial  instrument,  and  is  used 
in  some  cases  in  the  place  of  stenography,  the  correspondence  being 
dictated  to  the  instrument  and  then  reproduced  by  means  of  a 
typewriter. 

^W 

189.  Synthesis  of  sound-waves.  —  The  sound  of  a  tuning- 
fork  when  its  fundamental  is  reenforced  by  a  suitable  reso- 
nance-cavity, is  very  nearly  a  simple  tone. 

If  two  mounted  forks  forming  the  interval  of  an  octave  be 
sounded  together,  the  tones  proceeding  from  the  separate 
forks  soon  blend  together  into  one  sound,  to  which  we  assign 
the  pitch  of  the  lower  fork,  and  a  quality  richer  than  that  of 
either.  So  strong  is  the  illusion,  that  we  cannot  believe  the 
higher  fork  to  be  sounding,  until  we  ascertain  that  placing  a 
finger  on  its  prongs  so  as  to  damp  its  vibrations  at  once 
change's  the  timbre,  reducing  it  to  the  dull,  uninteresting 
quality  of  a  simple  tone.  If  to  these  two  forks  there  be 
added  a  fork  whose  interval  is  a  fifth  above  the  higher  of 
the  first  two  (i.e.  one  which  gives  the  second  harmonic  of  the 
first),  the  three  tones  blend  as  perfectly  as  did  those  of  the  two 
forks  ;  the  only  difference  perceptible  being  an  additional 
increase  of  richness. 


234  MOLAK   DYNAMICS. 

By  sounding  simultaneously  several  forks  of  different  but 
appropriate  pitch,  and  with,  the  requisite  relative  intensities, 
Helmholtz  succeeded  in  producing  sounds  peculiar  to  various 
musical  instruments,  and  even  in  imitating  most  of  the  vowel 
sounds  of  the  human  voice. 

Thus  it  appears  that  he  has  been  able  to  determine,  both 
analytically  and  synthetically,  that  the  quality  of  a  given  sound 
depends  upon  what  overtones  combine  with  its  fundamental  tone, 
and  upon  their  relative  intensities ;  or,  more  briefly,  upon  the 
form  of  the  sound-wave,  since  the  form  must  be  determined 
by  the  character  of  its  components. 

SECTION  XI. 

MUSICAL    INSTRUMENTS. 

190.  Classification   of  musical   instruments.  —  Musical   in- 
struments may  be  grouped  into  three  classes :   (1)  stringed 
instruments ;    (2)  wind  instruments,  in  which  the  sound  is 
due  to  the  vibration  of  columns  of  air  confined  in  tubes  ;  (3) 
instruments  in  which  the  vibrator  is  a  membrane  or  plate. 
The  first  class  has  received  its  share  of  attention  j  the  other 
two  merit  a  little  further  consideration. 

191.  Wind  instruments. 

Experiment  1.  —  Fig.  188  represents  a  set  of  Quincke's  whistles.  The 
tubes  are  of  the  same  size,  but  of  varying  length.  Blow  through  the 
small  tube  across  the  lips  of  the  large  tube  of  each  whistle  in  the  order  of 
their  lengths,  commencing  with  the  longest. 

Repeat  the  experiment,  closing  the  end  of  the  whistle  farthest  from 
you  with  a  finger,  so  as  to  make  what  is  called  a  "  closed  pipe."  1 

The  pitch  of  vibrating  air-columns,  as  well  as  of  strings, 

1  The  effect  of  interference  is  well  shown  with  these  tubes  by  blowing  at  the  same 
time  through  two  tubes  of  nearly  the  same  length.  A  peculiar  rattling  sound  is  the 
result.  A  very  different  result  is  obtained  when  two  tubes  a  fifth  apart  are  sounded 
together. 


CLASSIFICATION   OF    MUSICAL   INSTRUMENTS.        235 

varies  with  the  length,  and  (1)  in  both  stopped1  and  open1 
pipes  the  number  of -vibrations  is  inversely  proportional  to  the 
length  of  the  pipe.  (2)  An  open  pipe  gives  a  note  an  octave 
higher  than  a  closed  pipe  of  the  same  length. 


FIG. 188. 

Experiment  2.  — Take  some  of  the  longer  whistles,  and  blow  as  before, - 
gradually  increasing  the  force  of  the  current.  It  will  be  found  that  only 
the  gentle  current  will  give  the  full  musical  fundamental  tone  of  the  tube, 
—  a  little  stronger  current  producing  a  mere  rustling  sound ;  but  when 
the  force  of  the  current  reaches  a  certain  limit,  an  overtone  will  break 
forth ;  and,  on  increasing  still  further  the  power  of  the  current,  a  still 
higher  overtone  may  be  reached. 

1  The  terms  "  stopped  "  and  "  open  "  apply  to  only  one  end  of  the  pipe  ;  the  other, 
in  both  kinds,  is  always  open. 


236  MOLAR    DYNAMICS. 

Fig.  189  represents  an  open  organ-pipe  provided  with  a 
glass  window  A  in  one  of  its  sides.  -A  wire  hoop  B  has 
stretched  over  it  a  membrane,  and  the  whole  is  suspended  by 
a  thread  within  the  pipe.  If  the  membrane  be 
placed  near  the  upper  end,  a  buzzing  sound  pro- 
ceeds from  the  membrane  when  the  fundamental 
tone  of  the  pipe  is  sounded ;  and  sand  placed  on 
the  membrane  will  dance  up  and  down  in  a  lively 
manner.  On  lowering  the^nembrane,  the  buzzing 
sound  becomes  fainter,  till,  at  the  middle  of  the 
tube,  it  ceases  entirely,  and  the  sand  becomes 
quiet.  Lowering  the  membrane  still  further,  the 
sound  and  dancing  recommence,  and  increase  as 
the  lowrer  end  is  approached. 

(3)  When  the  fundamental  tone  of  an  open  pipe 
is  produced,  its  air-column  divides  into  two  equal 
vibrating  sections,  with  the  anti-nodes  at  the  extrem- 
ities of  the  tube,  and  a  node  in  the  middle. 

If  the  pipe  be  stopped,  there  is  a  node  at  the 
stopped  end  ;  if  it  be  open,  there  is  an  anti-node 
at  the  open  end;  and  in  both  cases  there  is  an 

anti-node  at  the  end  where  the  wind  enters,  which 
FIG.  189. 

is  always  to  a  certain  extent  open. 

A,  B,  and  C  of  Fig.  190  show  respectively  the  positions  of 
the  nodes  and  anti-nodes  for  the  fundamental  tone  and  first 
and  second  overtones  of  a  closed  pipe  ;  and  A',  B',  and  C' 
show  the  positions  of  the  same  in  an  open  pipe  of  the  same 
length.  The  distance  between  the  dotted  lines  shows  the 
relative  amplitudes  of  the  vibrations  of  the  air-particles  at 
various  points  along  the  tube.  Now  the  distance  between  a 
node  and  the  nearest  anti-node  is  a  quarter  of  a  wave-length. 
Comparing,  then,  A  and  Ar,  it  will  be  seen  that  the  wave- 
length of  the  fundamental  of  the  closed  pipe  must  be  twice 
the  wave-length  of  the  fundamental  of  the  open  pipe ;  hence 


SOUNDING    PLATES,  ETC. 


237 


the  vibration  period  of  the  latter  is  half  that  of  the  former; 
consequently  the  fundamental  of  the  open  pipe  must  be  an 
octave  higher  than  that  of  the  closed  pipe. 

In  the  three  cases  (A,  B,  and  C)  of  the  closed  tube,  the 
length  of  the  air-column  is  divided  into  £,  f ,  and  f  segments 
respectively ;  hence  the  corresponding  vibration-numbers  are 


B' 


c' 


FIG.  190. 

as  1  :  3  :  5,  etc.  Hence,  (4)  in  a  closed  tube,  only  those  over- 
tones whose  vibration-numbers  correspond  to  the  odd  multiples 
of  that  of  the  fundamental  are  present. 

In  the  cases  of  the  cloaod  tube,  the  length  of  the  air-column 
is  divided  into  f ,  f ,  and  f  segments  respectively ;  their  vibra- 
tion-numbers are  therefore  as  1:2:3,  etc.  Hence,  (5)  in  an 
open  tube,  the  complete  series  of  overtones  corresponding  to  its 
fundamental  may  be  present. 

192.    Sounding  plates,  etc. 


Experiment  3. — Fasten  with  a  screw  the  elastic  brass  plate  A  (Fig. 
191)  on  the  upright  support.     Strew  writing-sand  over  the  plate,  draw  a 


238 


MOLAR    DYNAMICS. 


rosined  bass  bow  steadily  and  firmly  over  one  of  its  edges  near  a  corner, 
and  at  the  same  time  touch  the  middle  of  one  of  its  edges  with  the  tip 
of  the  finger ;  a  musical  sound  will  be  produced,  and  the  sand  will  dance 
up  and  down,  and  quickly  collect  (1)  in  two  rows,  extending  across  the 
plate  at  right  angles  to  each  other.  Draw  the  bow  across  the  middle  of 


FIG.  191. 

an  edge,  and  touch  with  a  finger  one  of  its  corners  ;  the  sand  will  arrange 
itself  in  two  diagonal  rows  (2)  across  the  plate,  and  the  pitch  of  the  note 
will  be  a  fifth  higher.  Touch,  with  the  nails  of  the  thumb  and  fore- 
finger, two  points  a  and  b  (3)  on  one  edge,  and  draw  the  bow  across  the 
middle  c  of  the  opposite  edge,  and  you  will  obtain  additional  rows  and  a 
shriller  note. 

By  varying  the  position  of  the  point  touched  and  bowed, 
a  great  variety  of  patterns  can  be  obtained,  some  of  which 
are  represented  in  Fig.  1Q2.  It  will  be  seen  that  the  effect 
of  touching  the  plate  with  a  finger  is  to  prevent  vibration  at 
that  point,  and  consequently  a  node  is  there  produced.  The 
whole  plate  then  divides  itself  up  into  segments  with  nodal 
division  lines  in  conformity  with  the  node  just  formed.  The 
sand  rolls  away  from  those  parts  which  are  alternately  thrown 
into  crests  and  troughs,  to  the  parts  that  are  at  rest. 


INTERFERENCE. 


239 


193.    Interference. 

Experiment  4-  —  C  (Fig.  191)  is  a  tin  tube  made  in  two  parts  that 
telescope  one  within  the  other.  The  extremity  of  one  of  the  parts  ter- 
minates in  two  slightly  smaller  branches.  Bow  the  plate,  as  in  experi- 
ment 3  (1),  place  the  two  orifices  of  the  branches  over  the  segments 
marked  with  the  +  signs,  and  regulate  the  length  of  the  tube  so  as  to 
reenforce  the  note  given  by  the  plate,  and  set  the  plate  in  vibration. 


JL-J 


FIG.  192. 

Now  turn  the  tube  around,  so  that  one  orifice  may  be  over  a  +  segment, 
and  the  other  over  a  —  segment ;  the  sound  due  to  resonance  entirely 
ceases.  It  thus  appears  that  the  two  segments  marked  +  pass  through 
the  same  phases  together  :  likewise  the  phases  of  —  segments  correspond 
with  one  another ;  i.  e.  when  one  +  segment  is  bent  upward,  the  other 
is  bent  upward,  and  at  the  same  time  the  two  —  segments  are  bent 
downward ;  for,  when  the  two  orifices  of  the  tube  are  placed  over  two 
+  segments  or  two  —  segments,  two  condensations  followed  by  two  rare- 
factions pass  up  these  branches  and  unite  at  their -junction  to  produce  a 
loud  sound  ;  but  when  one  of  the  orifices  is  over  a  +  segment,  and  the 


240 


MOLAR    DYNAMICS. 


FIG.  193. 


other  over  a  —  segment,  a  condensation  passes  up  one  branch  at  the 
same  time  that  a  rarefaction  passes  up  the  other,  and  the  two  destroy 
each  other  when  they  come  together;  i.e.  the  two  sound-waves  combine 
to  produce  silence. 

194.  Bells.  —  A  bell  or  goblet  is  subject  to  the  same  laws 

°f  vibration  as  a  plate. 

Experiment  5.  —  Nearly  fill  a  large  goblet  with 
water,  strew  upon  the  surface  lycopodium  powder, 
and  draw  a  rosined  bow  gently  across  the  edge  of 
the  glass.  The  surface  of  the  water  will  become 
rippled  with  wavelets  (Fig.  193)  radiating  from  four 
points  90°  apart,  corresponding  to  the  centers  of 
four  venters  into  which  the  goblet  is  divided,  and 
the  powder  will  collect  in  lines  proceeding  from  the 
nodal  points  of  the  bell.  By  touching  the  proper 
points  of  a  bell  or  glass  with  a  finger-nail,  it  may  be 
made  to  divide  itself,  like  a  plate,  into  6,  8,  10,  etc. 

(always  an  even  number),  vibrating  parts. 

Experiment  6.  —  Remove  the  brass  plate  (Fig.  191)  from  its  support, 

and  fasten  the  bell  B  (Fig.  194)  on  the  support.     Bow  the  edge  of  the 

bell  at  some  point,  and  hold  the  open 

tube  C  in  a  horizontal  position  with  the 

center  of  one  of  its  openings  near  that 

point  of  the  edge  of  the  bell  which  is 

opposite  the  point  bowed.      The   tube 

loudly  reenforces  the  sound  of  the  bell. 

Move  the  tube  around  the  edge  of  the 

bell  and  find  its  nodes. 

Thrust  the  plunger  D  into  the  open 

end  E  of  the  tube,  and  find  what  part  of 

the  length  of  an  open  tube  a  closed  tube  should  be  to  reenforce  a  sound 

of  a  given  pitch. 

195.  Vocal  organs.  —  It  is  difficult  to  say  which  is  more  to 
be  admired,  the  wonderful  capability  of  the  human  voice  or 
the  extreme  simplicity  of  the  means  by  which  it  is  produced. 
The  organ  of  the  voice  is  a  reed  instrument  situated  at  the 
top  of  the  windpipe,  or  trachea.     A  pair  of  elastic  bands,  a  a 
(Fig.    195),  called  the   vocal  chords,  is  stretched    across    the 


FIG.  194. 


VOCAL    ORGANS.  241 

top  of  the  windpipe.  The  air-passage  b  between  these  chords 
is  freely  open  while  a  person  is  breathing :  but  when  he 
speaks  or  sings,  they  are  brought  together  so  as  to  form  a  nar- 
row, slit-like  opening,  thus  making  a 
sort  of  double  reed,  which  vibrates 
when  air  is  forced  from  the  lungs 
through  the  narrow  passage,  some- 
what like  the  little  tongue  of  a  toy 
trumpet.  The  sounds  are  grave  or 
high  according  to  the  tension  of  the 
chords,  which  is  regulated  by  muscu- 
lar action.  The  cavities  of  the  mouth 
and  the  nasal  passages  form  a  com- 
pound resonance  -  tube.  This  tube 
adapts  itself,  by  its  varying  width  and 

length,  to  the  pitch  of  the  note  produced  by  the  vocal  chords. 
Place  a  finger  on  the  protuberance  of  the  throat  called 
"  Adam's  apple,"  and  sing  a  low  note;  then  sing  a  high  note, 
and  you  will  observe  that  the  protuberance  rises  in  the  latter 
case,  thus  shortening  the  distance  between  the  vocal  chords 
and  the  lips.  Set  a  tuning-fork  in  vibration,  open  the  mouth 
as  if  about  to  sing  the  corresponding  note,  place  the  fork  in 
front  of  it,  and  the  cavity  of  the  mouth  will  resound  to  the 
note  of  the  fork,  but  will  cease  to  do  so  when  the  mouth 
adapts  itself  to  the  production  of  some  other  note.  The 
different  qualities  of  the  different  vowel  sounds  are  produced 
by  the  varying  forms  of  the  resonating  mouth-cavity,  the 
pitch  of  the  fundamental  tones  given  by  the  vocal  chords 
remaining  the  same.  This  constitutes  articulation. 

Strictly  speaking,  consonants  are  not  distinct  sounds  or  the  rep- 
resentatives of  sound.  They  represent  rather,  when  they  precede 
vowels,  the  different  positions  of  the  organs  of  speech  from  which 
(like  spring-boards,  as  it  were)  the  vowels  are  attacked.1  Following 

1  A  common  fault  with  young  singers  is  attempting  to  "  sing  the  consonants." 


242 


MOLAR    DYNAMICS. 


vowels,  they  represent  the  position  of  the  organs  of  speech  at  the 
interruption  of  the  vowel  sounds,  and  the  consequent  modifications 
of  these  sounds.  Consonants  are  accordingly  classified  into  labials, 
dentals,  gutturals,  etc.  The  more  care  exercised  in  placing  the 
organs  in  suitable  positions  for  attack  or  interruption  and  the  less 
sound  emitted  from  these  points  at  the  moment  of  attack,  the 
clearer  is  the  articulation.  Modulations  of  the  voice  in  conversa- 
tion take  place  usually  in  musical  intervals.  Singing  differs  from 
speaking  chiefly  in  the  manner  in  which  the  vocal  sounds  are  modi- 
fied. In  both,  the  sustained  sounds  are  vowel  sounds.  In  fact 
only  vowel  sounds  are  musical,  and  any  language  is  musical  in 
proportion  to  the  number  of  vowels  it  contains.  Thus  Greek  is  a 
more  musical  language  than  Latin,  and  Italian  than  German. 

196.    The  ear.  —  In  Fig.  196,  A  represents  the  external  ear- 


Fro.  196. 


passage ;  a  is  a  membrane,  called  the  tympanum,  stretched 
across  the  bottom  of  the  passage,  and  thus  closing  the  orifice 
of  a  cavity  b,  called  the  drum;  c  is  a  chain  of  small  bones 
stretching  across  the  drum,  and  connecting  the  tympanum 


THE    EAR.  243 

with  the  thin  membranous  wall  of  the  vestibule  e ;  ff  are  a 
series  of  semicircular  canals  opening  into  the  vestibule  ;  g  is 
an  opening  into  another  canal  in  the  form  of  a  snail-shell  g\ 
hence  called  the  cochlea  (this  is  drawn  on  a  reduced  scale)  ; 
d  is  a  tube  (the  Eustachian  tube]  connecting  the  drum  with 
the  throat;  and  h  is  the  auditory  nerve.  The  vestibule  and 
all  the  canals  opening  into  it  are  filled  with  a  transparent 
liquid.  The  drum  of  the  ear  contains  air,  and  the  Eustachian 
tube  forms  a  means  of  ingress  and  egress  for  air  through  the 
throat. 

Now  how  does  the  ear  hear  ?  and  how  is  it  able  to  dis- 
tinguish between  the  infinite  variety  of  form,  rapidity,  and 
intensity  of  aerial  sound-waves  so  as  to  interpret  correctly 
the  corresponding  quality,  pitch,  and  loudness  of  sound  ? 
Sound-waves  enter  the  external  ear-passage  A  as  ocean-waves 
enter  the  bays  of  the  sea-coast,  are  reflected  inward,  and 
strike  the  tympanum.  The  air-particles,  beating  against  this 
drum-head,  impress  upon  it  the  precise  wave-form  that  is 
transmitted  to  it  through  the  air  from  the  sounding  body. 
The  motion  received  by  the  drum-head  is  transmitted  by  the 
chain  of  bones  to  the  membranous  wall  of  the  vestibule. 
From  the  walls  of  the  spiral  passage  of  the  cochlea  project 
into  its  liquid  contents  thousands  of  fine  elastic  threads  or 
fibres,  called  "  rods  of  Corti."  As  the  passage  becomes  smaller 
and  smaller,  these  vibratile  rods  become  of  gradually  dimin- 
ishing length  and  size  (such  as  the  wires  of  a  piano  may 
roughly  represent),  and  are  therefore  suited  to  respond  sym- 
pathetically to  a  great  variety  of  vibration-periods.  This 
arrangement  is  sometimes  likened  to  a  "  harp  of  three  thou- 
sand strings  "  (this  being  about  the  number  of  rods).  The 
auditory  nerve  at  this  extremity  is  divided  into  a  large  num- 
ber of  filaments,  like  a  cord  unraveled  at  its  end,  and  one 
of  these  filaments  is  attached  to  each  rod.  Now,  as  the 
sound-waves  reach  the  membranous  wall  of  the  vestibule, 


244  MOLAR    DYNAMICS. 

they  set  it,  and  by  means  of  it  the  liquid  contents,  into  forced 
vibration,  and  so  through  the  liquid  all  the  fibers  receive  an 
impulse.  Those  rods  whose  vibration  periods  correspond 
with  the  periods  of  the  constituents  forming  the  compound 
wave  are  thrown  into  sympathetic  vibration.  The  rods  stir 
the  nerve  filaments,  and  the  nerve  transmits  to  the  brain  the 
impressions  received.  Much  as  a  piano  when  its  dampers  are 
raised  and  a  person  sings  into  it,  may  be  said  to  analyze  each 
sound-wave,  and  show  by  the  vibrating  strings  of  how  many 
tones  it  is  composed,  as  well  as  their  respective  pitches,  and  by 
the  amplitude  of  their  vibrations  their  respective  intensities  ; 
so,  it  is  thought,  this  wonderful  harp  of  the  ear  analyzes 
every  complex  sound-wave  into  a  series  of  simple  waves. 
Tidings  of  the  disturbances  are  communicated  to  the  brain, 
and  there,  in  some  mysterious  manner,  these  disturbances  are 
interpreted  as  sound  of  definite  quality,  pitch,  and  intensity. 


PART   II. 

MOLECULAR  DYNAMICS. —HEAT. 


SECTION  I. 

THEORY    OF    HEAT. 

IN  the  preceding  pages  the  theory  of  heat  has  been  several 
times  anticipated  ;  we  are  now  better  qualified  to  judge  of  its 
validity. 

197.    Enerc/y  of  mass  motion  convertible  into  heat. 

Experiment  1.  —  Hold  some  small  steel  tool  upon  a  rapidly  revolving 
dry  grindstone;  a  shower  of  sparks  flies  from  the  stone.  Place  a  ten- 
penny  nail  upon  a  stone  and  hammer  it  briskly  ;  it  soon  becomes  too  hot 
to  be  handled  with  comfort,  and  we  may  conceive  that  if  the  blows  were 
rapid  and  heavy  enough,  it  might  soon  become  red  hot.  Rub  a  desk 
with  your  fist,  and  your  coat-sleeve  with  a  metallic  button ;  both  the 
rubbers  and  the  things  rubbed  become  heated. 

You  observe  that  in  every  case  heat  is  generated  at  the 
expense  of  work  or  mass  energy ;  i.e.  mass  energy  destroyed 
becomes  heat.  When  the  brakes  are  applied  to  the  wheels  of 
a  rapidly  moving  railroad  train,  its  energy  is  converted  into 
heat,  much  of  which  may  be  found  in  the  wheels,  brake- 
blocks,  and  rails.  The  meteorites,  or  "  shooting-stars,"  which 
are  seen  at  night  passing  through  the  upper  air,  sometimes 
strike  the  earth,  and  are  found  to  be  stones  heated  to  a  light- 
giving  state.  They  become  heated  when  they  reach  our 
atmosphere,  in  consequence  of  their  motion  being  checked  by 
the  resistance  of  the  air. 


246 


MOLECULAR    DYNAMICS. 


198.    Heat  convertible  into  mass  energy. 

Experiment  2.—  Take  a  thin  glass  flask  A  (Fig.  197),  half  fill  it  with 
water,  and  fit  a  cork  air-tight  into  its  neck.  Perforate  the  cork,  insert  a 
glass  tube  bent  as  indicated  in  the  figure,  and  extend  it  into  the  water. 
Apply  heat  to  the  flask;  soon  the  liquid  rises  in  the 
C  J[_  11  tube,  and  flows  from  its  upper  end. 

Here  heat  produces  mechanical  motion,  and 
does  work  in  raising  a  mass  in  opposition  to 
gravitation.  Every  steam  engine  is  a  heat  en- 
gine, i.e.  the  power  of  steam  is  due  to  its  heat. 
The  steam  which  leaves  the  cylinder  of  an  en- 
gine, after  it  has  set  the  piston  in  motion,  is 
cooler  than  when  it  entered. 

It  will  be  shown  hereafter  that  in  all  cases 
when  work  is  done  by  heat  without  waste  or 
loss,  the  quantity  of  heat  consumed  is  propor- 
tional to  the  work  done ;  and,  conversely,  by 
the  performance  of, a  definite  quantity  of  work 
an  equivalent  quantity  of  heat  is  produced;  in 
other  words,  there  is  a  definite  quantitative 
relation  between  heat  and  work. 

If  heat  be  consumed,  and  mechanical  work  thereby  per- 
formed, we  are  justified  in  saying  that  heat  has  transformed 
itself  into  mass  energy ;  and,  conversely,  if  mass  energy  be 
expended  and  heat  thereby  produced,  we  may  say  that  mass 
energy  has  transformed  itself  into  heat. 

Now,  when  the  appearance  of  one  thing  is  so  connected 
with  the  disappearance  of  another  that  the  quantity  of  the 
thing  produced  can  be  calculated  from  the  quantity  of  that 
which  disappears,  we  conclude  that  the  one  is  formed  at  the 
expense  of  the  other,  and  that  they  are  only  different  forms 
of  the  same  thing.  We  have,  therefore,  reason  to  believe 
that  heat  is  of  the  same  nature  as  mass  energy ;  i.e.  it  is  only 
another  form  of  energy. 


.  197. 


THEORY    OF    HEAT.  247 

199.  Theory  of  heat.  —  A  body  loses  motion  in  communi- 
cating it.  The  hammer  descends  and  strikes  the  anvil ;  its 
motion  ceases,  but  the  anvil  is  not  sensibly  moved ;  the  only 
observable  effect  produced  is  heat.  Instead  of  a  motion  of 
the  hammer  and  anvil,  there  is  now  an  increased  vibratory 
motion  of  the  molecules  that  compose  the  hammer  and  anvil, 
—  simply  a  change  from  molar  to  molecular  motion.  Of  course, 
this  latter  motion  is  invisible.  According  to  this  view,  heat 
is  but  a  name  for  the  energy  of  vibration  of  the  molecules  of  a 
Jbody,  or,  briefly,  HEAT  is  MOLECULAR  KINETIC  ENERGY.  The 
science  which  treats  of  heat  as  a  form  of  energy  is  called 
thermodynamics. 

A  body  is  heated  by  having  the  motion  of  its  molecules 
quickened,  and  cooled  by  parting  with  some  of  its  molecular 
motion.  Cold  is  comparable  to  rest,  heat1  to  motion.  One 
body  is  hotter  than  another  when  the  average  kinetic  energy  of 
the  molecules  in  it  is  greater  than  in  the  other. 

As  late  as  the  beginning  of  the  present  century  heat  was  gen- 
erally regarded  as  "a  sensation  which  the  presence  of  fire"  (an 
"  igneous  fluid,"  "matter  of  heat,"  called  sometimes  "  caloric  ") 
"  occasions  in  animate  and  inanimate  bodies."  A  text-book  of  that 
period  makes  this  significant  statement :  "  There  is  fire  in  the  wood, 
and  there  is  air  in  the  field,  though  we  do  not  perceive  either  while 
at  rest.  Rubbing  two  pieces  of  wood  does  not  create  fire  any  more 
than  the  blowing  of  the  wind  creates  air.  Motion  renders  both 
,  perceptible."  The  former  and  the  more  modern  views  are  in  har- 
mony in  attributing  the  immediate  cause  of  the  sensation  to  motion. 
According  to  the  former  view,  the  sensation  is  produced  by  putting 
an  imaginary  fluid  in  motion ;  according  to  the  modern  view  it  is 
produced  by  quickening  the  motion  of  the  molecules  of  a  body. 

The  material  theory  became  untenable  when  it  was  shown  by 
Count  Rumford  2  that  the  quantity  of  heat  that  may  be  evolved  by 

1  Whenever  there  is  occasion  to  speak  of  the  sensation  which  heat  is  capable  of 
producing,  it  should  never  be  called  heat,  but  it  should  be  termed  a  heat  sensation  or 
the  sensation  of  heat. 

2  The  great  discovery  of  the  non-materiality  of  heat  was  made  by  an  American, 
Benjamin  Thompson  (Count  Rumford),  then  (1798)  residing  in  Munich.     This  dis- 


248  MOLECULAR    DYNAMICS. 

friction,  as,  for  instance,  in  the  boring  of  cannon,  is  practically 
limitless,  or  is  limited  only  by  the  mechanical  power  available. 
Now  according  to  this  theory,  when  a  piece  of  metal  is  rubbed  the 
caloric  is  rubbed  or  squeezed  out  of  it  ;  but,  as  Kumford  argued, 
"  anything  which  a  body  can  continue  to  furnish  without  limitation 
cannot  possibly  be  a  material  substance."  At  about  the  same  time 
Davy  showed  that  two  pieces  of  ice  may  be  melted  by  rubbing  them 
together  in  a  space  whose  temperature  is  below  the  melting  point. 

200.  Heat,  the  lowest  form  of  eneryy.  —  Heat  is  often  spoken 
of  as  the  "  lowest  form  of  energy."  That  is,  all  other  forms 
of  kinetic  energy  tend  to  transform  themselves  into  the 
"lower"  form  of  heat ;  as  water  tends  to  seek  a  lower  level. 
When  energy  is  spent  in  doing  work,  that  portion  which 
appears  in  no  other  form  appears  as  heat. 


SECTION  II. 

SOURCES    OF    HEAT. 

201.  Mechanical   energy   a   source   of  heat.  —  As    heat    is 
energy,  so  all  heat  must  originate    in  some  form  of  energy, 
I.e.  by  the  transformation  of  some   other  form  of  energy  into 
heat. 

In  the  preceding  section  it  was  shown  that  heat  may  be 
generated  at  the  expense  of  molar  motion,  i.e.  molar  motion 
checked  usually  results  in  molecular  motion,  the  energy  of 
which  is  heat.  By  friction,  by  compression,  by  percussion, 
or  by  any  process  by  Avhich  mass  motion  is  arrested,  heat  is 
mechanically  generated. 

202.  Chemical  union  a  source  ofheq/f. 

Experiment  1.  — Take  a  glass  test-tube  half  full  of  cold  water  and  pour 
into  it  one-fourth  its  volume  of  strong  sulphuric  acid.  The  liquid  almost 
instantly  becomes  so  hot  that  the  tube  cannot  be  held  in  the  hand. 

covery  lies  at  the  foundation  of  the  dynamical  theory  of  heat,  and  directly  led  to  the 
grandest  doctrines  of  modern  science,  the  correlation  and  the  conservation  of  energy. 
(See  p.304.) 


ANIMAL    HEAT    AND    MUSCULAR    MOTION.  249 

When  water  is  poured  upon  quicklime,  heat  is  rapidly 
developed.  The  invisible  oxygen  of  the  air  combines  with 
the  constituents  of  the  various  fuels,  such  as  wood,  coal,  oils, 
and  illuminating-gas,  and  gives  rise  to  what  we  call  burning, 
or  combustion,  by  which  a  large  amount  of  heat  is  generated. 
In  all  such  cases  the  heat  is  generated  by  the  combination  or 
clashing  together  of  molecules  of  substances  that  have  an 
affinity  (i.e.  an  attraction)  for  one  another.  Before  union 
the  energy  of  the  molecules  is  of  the  same  kind  as  that  of  a 
stone  on  a  shelf.  When  the  shelf  is  withdrawn,  gravity  con- 
verts the  potential  energy  of  the  stone  into  kinetic  energy  ; 
so  affinity  converts  the  potential  energy  of  the  molecules  into 
kinetic  energy  of  vibration,  i.e.  into  heat. 

When  a  definite  mass,  say  of  carbon  or  hydrogen,  is  burned, 
the  quantity  of  heat  produced  is  definite ;  hence  the  different 
fuels  have  a  definite  heat  value,  whicli  depends  in  part  upon 
the  combustion  equivalents  of  their  constituents. 

In  a  majority  of  cases  chemical  union  is  attended  by  the  evolu- 
tion of  heat ;  but  in  some  cases  work  has  to  be  done  by  heat  upon 
separate  elements  to  force  them  to  combine  either  directly  or  indi- 
rectly ;  hence  in  such  cases  the  union  is  attended  by  a  consumption 
or  disappearance  of  heat,  and  the  decomposition  of  compounds  thus 
formed  is  attended  by  an  evolution  of  heat. 

203.  Origin  of  animal  heat  and  muscular  motion.  —  The 
plant  finds  its  food  in  the  air  (principally  the  carbonic  acid 
in  the  air)  and  in  the  earth,  in  a  condition  analogous  to  that 
of  a  fallen  weight ;  but,  by  the  agency  of  the  sun's  radiation, 
work  is  performed  upon  this  matter  during  the  growth  of  the 
plant ;  potential  energy  is  stored  in  the  plant,  —  the  weight 
is  drawn  up  as  it  were.  The  animal  now  finds  its  food  in  the 
plant,  appropriates  the  potential  energy  stored  in  the  plant, 
and,  by  chemical  action,  chiefly  by  the  union  of  carbon  and 
hydrogen  with  oxygen,  this  energy  is  converted  into  the  en- 
ergy of  motion  in  the  form  of  heat  and  muscular  motion,  — 


250  MOLECULAR    DYNAMICS. 

the  weight  falls  and  its  energy  becomes  kinetic.  The  plant, 
then,  may  be  regarded  as  a  machine  for  converting  energy 
of  motion  received  from  the  sun  into  potential  energy  ;  the 
animal,  as  a  machine  for  transforming  it  again  into  energy 
of  motion. 

204.  The  sun  as  a  source  of  energy.  —  The  sun  is  not  only 
the  source  of  the  energy  exhibited  in  the  growth  of  plants,  as 
well  as  of  the  muscular  and  heat  energy  of  the  animal,  but  is 
also  the  source,  directly  or  indirectly,  of  very  nearly  all  the 
energy  employed  by  man  in  doing  work.     Our  coal-beds,  the 
results   of  the  deposit  of   vegetable  matter,  are  vast  store- 
houses  of  the  sun's   energy,  rendered  potential   during  the 
growth  of  the  plants  many  ages  ago.     Every  drop  of  water 
that  falls  to  the  earth  and  rolls  its  way  to  the  sea,  contribut- 
ing its  mite  to  the  immense  water-power  of  the  earth,  and 
every  wind  that  blows,  derives  its   power  directly  from  the 
sun. 

205.  Dissipation  of  energy. 

Work  is  done  by  heat  only  when  it  passes  from  a  higher  to  a 
lower  level,  i.e.  from  a  higher  temperature  to  a  lower  temperature. 
In  other  words  heat  would  not  be  available  for  doing  work  if  all 
matter  were  reduced  to  the  same  temperature.  Heat  has  a  ten- 
dency to  become  uniformly  diffused.  The  temperature  of  the  entire 
material  universe  tends  to  uniformity.  This  does  not  imply  that 
the  quantity  of  energy  in  the  universe  changes,  but  it  does  imply 
that  the  quantity  of  energy  available  to  man  for  doing  work  is 
diminishing.  A  railroad  car  with  its  furniture  and  all  objects  on 
board  the  car  may  be  considered  as  constituting  a  system  of  bodies. 
If  the  car  be  in  rapid  motion,  it  possesses  a  large  quantity  of  energy 
and  each  body  in  the  system  possesses  energy  proportionate  to  its 
mass,  but  the  energy  of  no  one  of  these  bodies  is  available  for  doing 
work  upon  another.  Why  ?  Because  all  have  like  velocities,  and 
no  one  can  impart  velocity  to  another.  So  in  a  system  where  all 
the  molecules  have  a  like  velocity,  there  can  be  no  transfer  of 
velocity  or  energy,  and  hence  no  work  can  be  done  within  the 
system  by  any  of  its  members. 


TEMPERATURE   DEFINED.  251 

Now  since  all  forms  of  energy  tend  toward  this  lower  form  of 
energy,  and  the  temperature  of  all  matter  tends  towards  a  uni- 
formity, and  since  in  proportion  as  uniformity  of  temperature  is 
reached  the  quantity  of  available  energy  in  the  universe  is  dimin- 
ished, we  are  forced  to  the  conclusion  expressed  by  Tait  that  "The 
available  energy  of  the  universe  tends  to  zero."  l  This  is  called  by 
Lord  Kelvin  the  Doctrine  of  Dissipation  of  Energy. 


SECTION  III. 

TEMPERATURE. 

206.  Temperature  defined.  —  The  words  warm,  hot,  cool, 
cold  are  associated  in  our  minds  with  a  series  of  sensations 
which  we  suppose  to  indicate  a  corresponding  series  of  states 
of  an  object  with  respect  to  heat;  that  is,  the  agent  which 
produces  these  sensations  is  heat.  These  are  all  temperature 
terms,  and  refer  to  the  state  of  an  object  with  reference  to 
heat.  Temperature  is  the  state  of  matter  in  respect  to  heat. 
When  the  quantity  of  heat  in  a  body  increases,  its  tempera- 
ture is  said  to  rise;  and  when  this  diminishes,  its  temperature 
is  said  to  fall.  The  relation  which  temperature  bears  to  heat 
is  analogous  to  that  which  hydrostatic  pressure  bears  to 
water.  Water  flows  from  high  level  to  low  level ;  heat  flows 
from  high  temperature  to  low  temperature.  When  we  pour 
water  into  a  vessel,  the  level  rises ;  so  heat  entering  a  body 
raises  its  temperature  (unless  it  is  transformed  in  doing  work). 
It  takes  more  water  to  fill  a  large  vessel  to  a  given  depth 
than  a  small  one  ;  it  takes  more  heat  to  raise  the  temperature 
of  a  body  of  large  mass  a  certain  amount  than  to  raise  the 
temperature  of  a  smaller  mass  of  the  same  substance  an  equal 

1  "In  the  beginning"  points  to  a  far  distant  period  when  all  the  energy  of  the 
physical  universe  was  in  the  available  form.  Physical  science  foresees  a  time  when 
all  available  energy  shall  become  zero  and  all  the  processes  of  nature  must  cease. 
"  The  marvellous  mechanism  of  nature  will  then  have  run  down,  and  no  further 
motion  or  life-process  will  be  possible  unless  some  new  order  intervenes  of  which, 
we  have  no  knowledge  or  conception." 


252  MOLECULAR    DYNAMICS. 

amount.  Depth  of  water  in  vessels  of  varying  size  is  not 
proportional  to  the  quantity  of  water  they  contain  ;  tempera- 
ture of  bodies  of  varying  mass  is  not  necessarily  proportional 
to  the  quantity  of  heat  they  contain.  For  example,  a  pint  of 
water  at  a  given  temperature  does  not  contain  the  same  quan- 
tity of  heat  as  a  gallon  of  water  at  the  same  temperature. 

If  body  A  be  brought  in  contact  with  body  B,  and  A  tend 
to  impart  heat  to  B,  then  A  is  said  to  have  a  higher  tempera- 
ture than  B.  Temperature  is  sometimes  spoken  of  as  the  state 
of  a  body  with  reference  to  its  tendency  to  communicate  heat  to, 
or  receive  heat  from,  other  bodies.  The  direction  of  the  flow 
of  heat  determines  which  of  two  bodies  has  the  higher  tem- 
perature. If  the  temperature  of  neither  body  rise  at  the 
expense  of  the  other,  then  both  have  the  same  temperature, 
or  are  said  to  be  in  thermal  equilibrium. 

Temperature  depends  on  the  average  kinetic  energy  of  the 
molecules.  The  temperature  of  a  substance  increases  propor- 
tionally to  the  mean  square  of  the  velocity  of  vibration  of  its 
molecules.  Bodies  have  the  same  temperature  when  the 
average  energy  of  the  molecules  of  each  is  the  same. 

207.    Temperature  a  relative  term. 

As  the  term  is  now  used,  temperature  is  a  relative  expression, 
not  an  expression  of  absolute  quantity.  It  is  regarded  rather  as  a 
quality  capable  of  greater  or  less  intensity,  than  as  a  quantity  which 
may  be  added  to  or  subtracted  from  other  quantities  of  the  same 
kind. 

For  instance,  if  the  temperatures  of  two  bodies  be  respectively 
25°  C.  and  35°  C. ,  we  say  with  truth  that  their  temperatures  differ 
by  10  centigrade  degrees ;  but  we  cannot  say  with  propriety  that  a 
temperature  of  25°  subtracted  from  a  temperature  of  35°  leaves  a 
temperature  of  10°,  or  that  the  two  temperatures  added  together 
give  a  temperature  of  00°. 

There  is  no  propriety  in  the  expression  "twice  as  hot."  The 
term  temperature  is  similar  to  the  term  hardness,  insomuch  as  we 
are  able  to  construct  a  scale  for  both,  so  that  a  body  may  have  a 
definite  place  in  the  scale  and  be  less  hot  or  less  hard  than  some- 


OF    A    THERMOMETER.  253 

thing  above  it,  and  yet  we  are  not  able  to  estimate  either  tempera- 
ture or  hardness  quantitively. 

SECTION  IV. 

THERM  O  M  KTK  Y. 

208.  Use  of  a  thermometer.  —  A  thermometer  is  an  instru- 
ment for  indicating  temperature,  i.e.  the  difference  between 
the  temperature  of  a  given  body  and  some  standard  tempera- 
ture (§  211).     For  the  difference  between  two  standard  tem- 
peratures, such  as  the  melting  point  of  ice  and  the  boiling- 
point  of  water,  is  one  capable  of  accurate  subdivision  into 
any  number  of  equal  parts,  which  form  successive  equal  steps 
from  the  lower  to  the  higher  temperature. 

209.  Temperature  indicated  by  expansion.  —  The  effects  of 
expansion  by  heat  are  well  illustrated  in  the  common  ther- 
mometer.    As  its  temperature  rises,  both  the  glass  and  the 
mercury  expand ;  but,  as  liquids  in  general  are  more  expansi- 
ble than  solids,  the  mercury  expands  much  more  rapidly  than 
the  glass,  and  the  apparent  expansion  of  the  mercury,  shown  by 
its  rise  in  the  tube,  is  the  difference  betiveen  the  actual  increase  of 
volume  of  the  mercury  and  that  of  the  capacity  of  the  glass  ves- 
sel containing  it.     The  thermometer,  then,  primarily  indicates 
changes  of  volume  ;  but  as  changes  of  volume  in  this  case  are 
caused  by  changes  of  temperature,  it  is  commonly  used  for 
the  more  important  purpose  of  indicating  temperature. 

If  a  thermometer  be  brought  into  intimate  contact  with  a 
body  whose  temperature  is  sought,  as,  for  instance,  a  liquid 
into  which  it  is  plunged,  or  the  air  in  a  room,  the  mercury  in 
the  tube  rises  or  falls  until  it  reaches  a  certain  point,  at 
which  it  remains  stationary.  We  then  know  that  it  is  in 
thermal  equilibrium  with  the  surrounding  body.  Hence  the 
read! at/,  as  it  is  called,  of  the  thermometer  indicates  not  only 
the  temperature  of  the  mercury,  but  of  the  surrounding  body. 


254  MOLECULAR    DYNAMICS. 

210.  Construction  of  a  thermometer,  —  A  thermometer  con- 
sists generally  of  a  glass  tube  of  capillary 1  bore,  terminating 
at  one  end  in  a  bulb.     The  bulb  and  part  of  the  tube  are  rilled 
with  mercury,  and  the  space  in  the  tube  above  the  mercury 
is  a  partial  vacuum.     On  the  tube,  or  on  a  plate  of  metal 
behind  the  tube,  is  a  scale  to  show  the  hight  of  the  mercurial 
column. 

211.  Standard   temperatures.  —  That  a  thermometer  may 
indicate   any  definite  temperature,   it   is  necessary  that  its 
scale  should  relate  to  some  definite  and  unchangeable  points 
of  temperature.     Fortunately  Nature  furnishes  us  with  two 
convenient  standards.     It  is  found  that  under  ordinary  atmos- 
pheric pressure  ice  always  melts  at  the   same  temperature, 
called  the  melting  point.     Again,  the  temperature  of  steam 
rising  from  boiling  water  under  the  same  pressure  is  always 
the  same. 

212.  Graduation  of  thermometers.  —  First,  the  bulb  of  a 
thermometer  is  placed  in  melting  ice  (Fig.  198)  and  allowed 
to  stand  until  the  surface  of  the  mercury  becomes  stationary, 
and  a  mark  is  made  upon  the  stem  at  that  point,  which  indi- 
cates the  melting  point.     Then  the  instrument  is  suspended 
in  steam  rising  from  boiling  water  (Fig.  199),  so  that  all  but 
the  very  top  of  the  column  is  in  the  steam. 

The  bulb  is  placed  in  a  metallic  vessel,  M,  with  a  narrower 
upper  part,  A.  This  narrower  part  is  surrounded  by  a  larger 
part,  B.  By  observing  the  arrows  it  is  seen  that  steam  sur- 
rounds the  inner  part,  and  thus  prevents  its  cooling  ;  it 
escapes  by  the  tube  D.  The  orifice  of  D  is  large  enough  to 
allow  the  steam  to  escape  freely,  and  thus  prevent  a  pressure 
inside  the  vessel  greater  than  the  atmospheric  pressure.  To 
guard  against  such  a  contingency  a  pressure  gauge  m  is  in- 
serted in  the  vessel.  The  liquid  in  both  arms  of  the  gauge 

1  In  consequence  of  refraction  of  light  at  the  cylindrical  surface  of  the  glass  tube, 
the  diameter  of  the  cylinder  of  mercury  in  the  bore  appears  magnified. 


GRADUATION   OF   THERMOMETERS. 


255 


must  be  kept  at  the  same  level  throughout  the  operation. 
The  mercury  rises  in  the  stem  of  the  thermometer  until  its 
temperature  becomes  the  same  as  that  of  the  steam,  when  it 
becomes  stationary.  A  barometer  is  consulted,  and  due  allow- 
ance having  been  made  for  atmospheric  pressure  at  the  time, 
a  mark  is  placed  on  the  stem  to  indicate  the  boiling  point. 
This  boiling  point  is  the  temperature  of  steam  at  a  pressure 


FIG.  198. 


FIG.  199. 


of  760  mm  of  mercury  at  0°  C.  in  the  latitude  of  Paris  (48° 
50'),  60  meters  above  sea-level.  Then  the  space  between  the 
two  points  found  is  divided  into  a  convenient  number  of 
equal  parts  (provided  that  the  bore  of  the  tube  is  of  uniform 
diameter)  called  degrees,  and  the  scale  is  extended  above  and 
below  these  points  as  far  as  is  desirable. 

Two  methods  of  division  are  adopted  in  this  country  (see  a 
and  b,  Fig.  200)  :  by  one,  the  space  is  divided  into  180  equal 
parts,  and  the  result  is  called  the  Fahrenheit  scale,  from  the 
name  of  its  designer  ;  by  the  other,  the  space  is  divided  into 


256 


MOLECULAR    DYNAMICS. 


;  7  n 

.  1:. 


100  equal  parts,  and  the  resulting  scale  is  called  rentigrade, 
which   means   o?*e  hundred  steps.      In   the   Fahrenheit  scale, 
which  is  generally  employed  for  ordinary  household  purposes, 
5        a  the  melting  and   boiling  points   are   marked 

respectively  32°  and  212°.  The  0  of  this 
scale  (32°  below  melting  point),  which  is 
about  the  lowest  temperature  that  can  be  ob- 
tained by  a  mixture  of  snow  and  salt,  was 
incorrectly  supposed  to  be  the  lowest  temper- 
ature attainable.  The  centigrade  scale,  which 
is  generally  employed  by  scientists,  has  its 
melting  and  boiling  points  more  conveniently 
marked,  respectively  0°  and  100°.  A  temper- 
ature below  0°  in  either  scale  is  indicated 
by  a  minus  sign  before  the  number.  Thus. 
- 12°  F.  indicates  12°  below  0°  (or  44°  below 
melting  point),  according  to  the  Fahrenheit 
scale.  Under  F.  and  C.  (in  the  left  column, 
Fig.  201),  the  two  scales  are  placed  side  by 
side,  so  as  to  exhibit  at  intervals  a  compara- 
tive view.  The  Fahrenheit  and  centigrade 
scales  agree  at  —  40°,  but  diverge  both  ways 
from  this  point. 

213.  Conversion  from  one  scale  to  the  other. 
-Since  100°  C.  =  180°  F.,  5°  C.  =  9°  F.. 
or  1°  C.  =  f  of  1°  F.  Hence,  to  convert 
centigrade  degrees  into  Fahrenheit  degrees, 
we  multiply  the  number  by  f  ;  and  to  convert 
Fahrenheit  degrees  into  centigrade  degrees  we  multiply  by  |. 
In  finding  the  temperature  on  one  scale  that  corresponds  to  a 
given  temperature  on  the  other  scale,  it  must  be  remembered 
that  the  number  that  expresses  the  temperature  on  a  Fahren- 
heit scale  does  not,  as  it  does  on  a  centigrade  scale,  express 
the  number  of  degrees  above  melting  point.  For  example, 


FIG.  200. 


DEVELOPMENT    OF    THE    THERMOMETER. 


257 


52°  on  a  Fahrenheit  scale  is  not  52°  above  melting  point,  but 
52°  —  32°  =  20°  above  it. 

Hence,  to  reduce  a  Fahrenheit  reading  to  a  centigrade  read- 
ing, first  subtract  32  from  the  given  number,  and  then  multiply 
by  f .  Thus, 

f(F-32)  =  C. 


To  change  a  centigrade 
reading  to  a  Farhenheit 
reading,  first  multiply  the 
(liven  number  by  f  ,  and  then 
add  32.  Thus. 


214.  Development  of  the 
thermometer. 

Though  the  invention  of 
the  thermometer  has  been 
ascribed  to  various  scien- 
tific men,  it  did  not  assume 
a  practical  shape  until  1620, 
at  the  hands  of  Drebel,  a  • 
Dutch  physician.  Halley 
substituted  mercury  for  Lc 
spirit  in  1730  ;  Rlaumur 
of  Paris  modified  the  instru- 
ment in  1730,  and  Fahren-  FlG-  201' 

heit  of  Danzig  in  1749;  Celsius  of  Upsala,  Sweden,  improved  it  in 
1742  by  adding  the  scale  now  known  as  centigrade.1 

215.  Self  -register  in  </,  or  maximum  and  minimum  thermome- 
ters. 

These  are  thermometers  which  enable  us  to  ascertain  the  highest 
or  lowest  temperature  to  which  they  have  been  exposed  in  a  given 

1  The  Reaumur  thermometer  is  used  generally  in  Germany,  the  centigrade  in 
France,  and  the  Fahrenheit  in  England.  "A  prophet  is  not  without  honor  save  in 
his  own  country." 


c. 

Tin  melts  233C 

- 

II 

F.            & 

451°           506° 

- 

f! 

ii 

878.4° 

Water  boils  100° 

212°          373° 

639.4° 

Alcohol  boils  78° 

- 

172.4°        351° 

- 

599.8° 

Ether  boils  35° 

- 

95°             308° 

- 

522.4° 

Ice  melts  0° 

- 

320               273° 

- 

459.4° 

Mercurr-freezes-38.80 

- 

-37.9°      234.2° 

" 

421  .3° 

Alcohol  freezes-j:W.5° 

- 

-202.9°     142.5° 

- 

256.5° 

niperatureyet  attained 
ited  to  be  about-220° 

- 

-364°            53° 

- 

95° 

-273° 

_ 

-459.4°           o° 

. 

0° 

258  MOLECULAR   DYNAMICS. 

interval  of  time,  ordinarily  a  day.  The  maximum  thermometer 
(the  lower  one,  Fig.  202)  is  an  ordinary  mercurial  thermometer, 
except  that  the  bore  of  the  tube  near  the  bulb  is  reduced  in  such  a 
way  that  while  the  expansion  of  the  mercury  is  sufficient  to  force 
the  liquid  past  the  constriction,  the  cohesion  of  the  liquid  is  insuffi- 
cient to  draw  it  back  again  when  the  temperature  falls.  To  set  the 
thermometer  it  is  placed  in  a  vertical  position  and  shaken.  This 
causes  the  mercury  to  return  past  the  constriction  to  the  bulb,  and 
then  the  instrument  indicates  the  same  temperature  as  that  of  the 
air.  The  instrument  is  then  placed  in  a  horizontal  position  as  shown 
in  the  figure. 

The  minimum  thermometer  (the  upper  one,  Fig.  202)  contains 
alcohol,  since  the  freezing  point  of  alcohol  is  far  below  that  of 
mercury.  The  bore  of  the  tube  contains  a  little  index  of  metal  or 
black  glass  which  moves  with  a  little  friction  in  the  tube.  It  is 
entirely  enveloped  in  the  spirit,  and  the  action  is  as  follows :  The 


FIG.  202. 

instrument  is  set  by  placing  it  first  in  an  inverted  position  to  allow 
the  index  to  run  down  the  tube  to  the  end  of  the  liquid  column, 
and  it  is  then  placed  in  a  horizontal  position.  If  the  temperature 
rise,  the  spirit  flows  past  the  index  without  disturbing  it.  If  the 
temperature  fall  below  that  at  which  the  instrument  was  set,  the 
capillary  action  between  the  spirit  and  the  index  is  such  as  to  pre- 
clude its  leaving  the  index ;  accordingly  this  is  drawn  back  with  the 
spirit,  its  upper  end  being  always  flush  with  the  extremity  of  the 
liquid  column,  and  ultimately  marking  the  lowest  temperature 
reached  by  the  column. 

216.    Requirements  of  a  thermometric  substance. 

The  substances  most  commonly  employed  for  thermometric  pur- 
poses are  mercury,   alcohol,   and   air.      The  requirements  are  as 


invention  of  the  thermometer  marks  an  epoch  in  science,  for  it 
las  permitted  of  obtaining  a  knowledge  of  the  laws  that  govern 
s  phenomena.     The  first  idea  of  it  is  perhaps  due  to  the  celebrated 
3lmont,  who  devised  an  apparatus  which,  to  use  his  words,  was  "to       059 
hat  the  water  contained  in  a  bulb  attached  to  a  hollow  rod  rises  or 
Is  according  to  the  temperature  of  the  surrounding  medium."     In 
enteenth  century,  the  necessity  of  an  apparatus  adapted  for  meas-    In  this 
lie  differences  of  the  temperature  was  so  greatly  felt  that  Galileo,  ement . 
Scarpi,  Fludd,  Borelli,  and  other  scientists  of  the  epoch  devoted 
Ives  in  this  direction  to  researches  that  were  not  always  crowned  Pansion 
iccess.     It  is  not  till  1621  that  we  find  a  beginning  of  the  solution  ?  points 
ixperiments  of  a  Dutchman,  Cornelius  Van  Drebbel.     This  physi-  f  them, 
lermometer  consisted  of  a  tube  filled  with  air,  closed  at  its  upper  ,ansion 
ty  and  dipping  at  its  other  exremity  (which  was  open)  in  a  bottle 
ing  nitric  acid  diluted  with  water.     According  as  the  external  tern-  !  have  a 
erose  or  fell,  the  air  in  the  tube  increased  or  diminished  in  volume,  ^mpera- 
nsequently  the  liquid  descended  or  rose.     This  instrument,  called  alcohol 
ndare  vitreum  (indicating  glass)  by  its  inventor,  constituted  what    ghouid 
3e  been  called  an  air  thermometer;  but,  as  its,  graduation  was  based    k 

0  definite  principle,  it  was  incapable  of  furnishing  any  comparable  *•     (4) 
.     Along  about  1650  the  members  of  the  Accademia  del  Cimento,  iture  is 
3nce,  introduced  into  the  thermometer  certain  improvements  that  16rcury 

nearly  the  form  that  it  has  to-day;  and  its  principle  was  based 
le  expansion  of  liquids.     The  tube  was  filled  with  colored  alcohol.  /C(lmre 
r  to  graduate  it,  it  was  taken  to  a  cellar  and  the  place  was  marked  V  than 
;he  liquid  came  to  a  rest.     Then,  starting  from  this,  the  portions 

1  above  and  below  the  mark  were  divided  into  100  equal  parts. 
•  be  seen,  it  was  impossible  with  such  a  system  to  construct  two 
lents  that  should  agree.     Nevertheless,  it  was  the  only  apparatus 
,s  made  use  of  for  half  a  century.     Finally,  in  the  latter  part  of 
enteenth  century,  the  physicist  Renaldini,  of  Pisa,  a  professor  at  ard  for 
proposed  that  all  thermometers  should  take  the  freezing  degree  of  >f  ther- 
s  a  fixed  point,  and,  as  a  second  fixed  point,  that  to  which  alcohol 

a  tube  dipping  in  melted  butter,  the  intervening  space  to  be  divided 
aal  parts.     From  this  epoch,  then,  dates  the  present  thermometer,    degree 
i  first  instrument  due  to  this  innovation  dates  back  to  1701.     This  accom- 
istructed  by  Newton,  and  was  the  first  thermometer  giving  coin-  rhere  it 
readings  that  had  been  devised.     The  liquid  that  he  adopted  was  0  v,een 
oil,  which  is  capable  of  supporting  a  higher  temperature  than  s 
without  boiling,  and  his  fixed  point  of  graduation  for  the  upper    neces- 
ras  the  heat  of  the  human  body,  and  for  the  lower,  the  point  at  is  lain 
the  oil  stops  at  the  moment  of  its  congelation.     A  search  soon    causes 

0  be  made  for  a  thermometric  agent  other  than  oil  (which  was  too         - 
expanded  by  heat  and  which  congeals  at  but  a  slightly  elevated 
iture),  and,  in  1714,  Gabriel  Fahrenheit,  of  Dantzig,  almost  com-    l  ther- 
solved  the  problem  in  the  construction  of  the  thermometer  that    n  of  a 
;ars  his  name.     This  was  immediately  adopted  in  Germany  and   5  com- 
d  (where  it  is  still  employed)  and  was  introduced  into  France. 

ng  about  1730  scientists  gave  preference  to  the  one  that  Reaumur    ( 
stf  devised.     Finally,  in  1741,  Celsius,  a  professor  at  Upsal,  con- 

1  the  instrument  called  the  centigrade  thermometer.     The  three 

ned  instruments  are  the  ones  most  commonly  used,  and  differ  only  yrom- 
^raduation  of  each. — La  Science  en  Famille. 

Any  contrivance  xor  determining  temperature  above  the  range 
of  a  mercurial  thermometer  (327°  C.)  is  called  a  pyrometer.  There 
are  several  varieties.  Some  are  constructed  on  the  principle  that 


(the  lower  one, 

except  that  the  >P  art  of 

way  that  while 

y 


aas«^?s£al^*?2 

*3»*'*«'*»  hart  "1 


dent  to  draw  it  -eed.    TWs 

thermometer  it  £  universal.     Upon  It 

causes  the  mere 

then  the  instrun      "1^ 


a.coho,,  since 


aiconoi,  since    w   -"•««  per  1,000  inhabit     1J     x  lye  city  to  the     h 


instrument 

the  •»*« 

and  it  is  th 


£»v^,'^«._  .    Ai*t;.ie  is  no  o\7o*^»-  "      c  ^oiaen    rJnto  i „,   J 


and  it  is  th  middle  of  p^f  hat  of  Iast  Jea7  AT?  W^sterlv  tendency 
rise,  the  s  NewOrl°e^e^adL?d  B^'a^eTa^  ^J^S 
temperatu  trough  the  various  QaSlspread  tot  abont  %  £fter  ra 

spirit,  its  ticular  vicinTty  To^U^ith  ^^SS^?*,  mte-  A 
liquid  co^assumed  aTmoJt  the"  WeSt'  at  ^W^fe  ^.Jt  aPProa, 
reached  *1^^^ 

216.    Requirements  of  a  thermometric  substance. 

The  substances  most  commonly  employed  for  thermometric  pur- 
poses are  mercury,   alcohol,   and   air.      The  requirements  are  as 


STANDARD    THERMOMETER.  259 

follows  :  (1)  The  substance  should  be  uniformly  expansible.  In  this 
respect  the  air-thermometer  most  nearly  meets  the  requirement; 
but  there  are  great  inconveniences  attending  its  use.  The  expansion 
of  mercury  is  nearly  uniform  between  the  melting  and  boiling  points 
on  the  scale  and  for  a  considerable  range  on  each  side  of  them. 
Alcohol,  on  account  of  lack  of  uniformity  in  its  rate  of  expansion, 
is  ill-adapted  for  this  use.  (2)  A  thermometric  liquid  should  have  a 
high  boiling  point.  A  mercury  thermometer  will  indicate  tempera- 
ture as  high  as  about  327°  C.  (620°  F.).  The  boiling  point  of  alcohol 
is  below  that  of  water.  (3)  The  freezing  point  of  the  liquid  should 
be  low.  This  furnishes  the  only  reason  for  the  use  of  alcohol.  (4) 
The  sensibility  of  the  liquid  to  sudden  changes  of  temperature  is 
of  importance.  On  account  of  the  high  conductivity  of  mercury 
and  its  low  specific  heat  (§  221),  a  mercurial  thermometer  acquires 
thermal  equilibrium  with  the  surrounding  body  more  quickly  than 
any  other  liquid  thermometer. 

217.  Standard  thermometer. 

As  its  name  indicates,  this  instrument  is  used  as  a  standard  for 
reference,  and  for  testing  from  time  to  time  the  accuracy  of  ther- 
mometers used  for  ordinary  observations. 

It  is  a  thermometer  which  has  been  compared  for  every  degree 
with  an  air  thermometer,  and  has  a  table  of  corrections  accom- 
panied with  a  certificate  of  authority  from  the  laboratory  where  it 
was  compared.  Owing  to  the  fact  that  glass  after  having  been 
fused  does  not  immediately  return  to  its  normal  density,  it  is  neces- 
sary to  use  for  a  standard  thermometer  a  tube  which  has  lain 
several  years  after  being  filled.  The  contraction  of  the  bulb  causes 
a  thermometer  to  read  too  high  if  it  was  graduated  before  the 
contraction  was  completed.  The  result  of  this  defect  in  a  ther- 
mometer is  called  the  displacement  of  zero.  The  graduation  of  a 
standard  thermometer  is  made  on  the  glass  stem,  and  thus  com- 
plication due  to  difference  of  dilation  of  different  substances  is 
avoided. 

218.  Determination  of  extremely  high  temperatures.    Pyrom- 
eter. 

Any  contrivance  for  determining  temperature  above  the  range 
of  a  mercurial  thermometer  (327°  C.)  is  called  a  pyrometer.  There 
are  several  varieties.  Some  are  constructed  on  the  principle  that 


260 


MOLECULAR    DYNAMICS. 


FIG.  203. 


a  change  of  temperature  affects  the  electrical 
resistance  of  a  metal.  A  hydropyrometer  indi- 
cates high  temperatures  by  the  number  of 
degrees  a  given  mass  of  water  is  raised,  by 
the  immersion  in  it  of  a  platinum  ball  of 
known  weight  after  it  has  acquired  the  tem- 
perature, for  instance,  of  a  furnace  or  oven 
to  be  tested.  Daniell's  pyrometer  is  one  of 
the  most  useful  in  practice.  The  indications 
are  obtained  from  the  difference  in  expan- 
B  sion  of  a  platinum  bar  A  (Fig.  203)  and  a 
tube  of  black  lead  B  in  which  the  bar  is  con- 
tained. The  index  C  moves  over  the  scale 
D  as  the  metal  rod  expands.  The  degrees 
on  this  scale  are  easily  converted  into  those  of 
Fahrenheit  or  centigrade  scales. 

SECTION  V. 

CALORIMETRY. 

219.  Distinction  between  the  questions  "  how  hot""  and  "how 
much  heat"    -The  former,  like  the  question  "how  sweet," 
when  applied  to  a  solution  of  sugar,  is  answered  only  rela- 
tively.    The  latter,  like  the  question  "how  much  sugar  in 
the  solution,"  is  answered  quantitively.     Sweetness  and  tem- 
perature are  independent  of  the  mass  of  the  body.     Quantity 
of  sugar  depends  upon  the  sweetness  and  the  mass  of   the 
liquid  ;  quantity  of  heat  depends  upon  the  temperature  and 
the  mass  of  the  body.     A  pint  of  boiling  water  is  as  hot  as 
a  gallon  of  the  same ;  but  the  latter  contains  eight  times  as 
much  heat.     Temperature  depends  on  the  average  kinetic  ener<jij 
of  the  molecules.     Quantity  of  heat  is  the  product  of  th'e  aver  aye 
kinetic  energy  of  the  molecules  multiplied  by  the   number  of 
molecules. 

220.  Thermal  units.  —  A  thermal  unit  is  the  quantity  of 
heat  required  to  produce  a  definite  effect.     The  thermal  unit 
generally  adopted  is  the    calorie,   which  is  the   quantity  of 


HEAT    CAPACITY,    SPECIFIC    HEAT.  261 

heat  necessary  to  raise  one  kilogram  of  water  from  4°  to  5° 
C.1  The  thermal  unit  in  the  C.  G.  S.  system  is  the  gram-calorie, 
sometimes  called  the  smaller  calorie,  which  is  the  quantity  of 
heat  required  to  raise  one  gram  of  water  from  4°  to  5°  C.  In 
defining  a  thermal  unit  it  is  necessary  to  state  the  tempera- 
tures between  which  the  water  is  raised,  because,  although 
the  quantity  of  heat  required  to  raise  a  given  quantity  of 
water  one  degree  is  very  nearly  the  same  at  different  tempera- 
tures, and  in  practice  is  usually  regarded  as  the  same,  yet  the 
quantity  required  is  a  very  little  greater  at  high  temperatures 
than  at  low  temperatures  (see  §  223).  The  operation  of  meas- 
uring heat  is  called  calorimetry. 

221.  Heat  capacity,  specific  heat.  —  The  expression  heat 
capacity  applied  to  a  body  refers  to  the  quantity  of  heat 
necessary  to  raise  the  temperature  of  the  body  1°.  The 
expression  specific  heat  is  applied  only  to  some  particular 
substance  and  refers  to  the  quantity  of  heat  required  to  raise 
one  kilogram  of  that  substance  from  4°  to  5°  C.  It  is  apparent 
that  the  specific  heat  of  a  substance  is  the  heat  capacity  of  1  unit 
of  mass  of  that  substance. 

Experiment  1.  —  Mix  1  K  of  water  at  0°  with  1  K  at  20° ;  the  tempera- 
ture of  the  mixture  becomes  10°.  The  heat  that  leaves  1  K  of  water 
when  it  falls  from  20°  to  10°  is  just  capable  of  raising  1  K  of  water  from 
0°  to  10°. 

Experiment  2.  —  Take  (say)  300  g  of  sheet  lead,  make  a  loose  roll  of  it, 
and  suspend  it  by  a  thread  in  boiling  water  for  about  five  minutes,  that 
it  may  acquire  the  same  temperature  (100°  C.)  as  the  water.  Remove 
the*  roll  from  the  hot  water,  and  immerse  it  as  quickly  as  possible  in 
300  g  of  water  at  0°,  and  introduce  the  bulb  of  a  thermometer.  Note  the 
temperature  of  the  water  when  it  ceases  to  rise,  which  will  be  found  to 

1  Authorities  do  not  agree  on  the  temperature  limits  for  this  unit.  Some  German 
authorities  give  15°  to  16C  C.  Regnault  chose  0°  to  1°  C.,  and  this  has  been  quite 
generally  adopted  in  scientific  treatises.  There  seem,  however,  to  be  good  reasons 
for  a  departure  from  this  custom,  and  we  have  chosen  the  limits  proposed  by 
Glazebrook  in  his  recent  treatise  on  Heat,  viz.,  4°  to  5°  C. 


262  MOLECULAR   DYNAMICS. 

be  about  3°  (accurately  3.3°  +).  The  lead  cools  very  much  more  than  the 
water  warms.  The  temperature  of  lead  falls  about  33°  for  every  degree 
an  equal  mass  of  water  is  warmed. 

From  the  first  experiment  we  infer  that  a  body  in  cooling 
a  certain  number  of  degrees  gives  to  surrounding  bodies  as 
much  heat  as  it  takes  to  raise  its  temperature  the  same  number 
of  degrees.  From  the  second  experiment  we  learn  that  the 
quantity  of  heat  that  raises  1  K  of  lead  from  3.3° -f  to  100°, 
when  transferred  to  water,  can  raise  1  K  of  water  only  from 
0°  to  3.3°.  Hence  we  conclude  that  equal  quantities  of  heat, 
applied  to  equal  masses  of  different  substances,  raise  their 
temperatures  unequally. 

If  equal  masses  of  mercury,  alcohol,  and  water  receive 
equal  quantities  of  heat,  the  mercury  will  rise  30°,  and  the 
alcohol  nearly  2°,  for  every  degree  the  water  rises.  From 
this  we  infer  that  to  raise  equal  masses  of  each  of  these 
substances  1°  requires  30  times  as  much  heat  for  the  water 
as  for  the  mercury,  and  twice  as  much  as  for  the  alcohol. 
Since  a  given  quantity  of  heat  affects  the  temperature  of  a 
given  mass  of  water  less  than  that  of  an  equal  mass  of  mer- 
cury or  alcohol,  water  is  said  to  have  greater  specific  heat 
than  these  substances.  It  is  also  apparent  that  a  given  mass 
of  water  in  cooling  imparts  to  surrounding  bodies  more  heat 
than  the  same  masses  of  mercury  and  alcohol  would  impart 
in  cooling  the  same  number  of  degrees,  in  proportion  to  its 
greater  specific  heat. 

222.    Method  of  measuring  specific  heat. 

There  are  at  least  four  methods  practiced,  only  one  of  which,  the 
"method  of  mixtures,"  will  be  considered.  A  known  mass  m  (in 
kilograms)  of  the  substance  of  which  the  specific  heat  is  required  is 
taken,  as  in  Experiment  2,  and  heated  to  a  known  temperature  ti 
(C) ;  then  it  is  mixed  with  (or  immersed  in)  a  known  mass  of  water 
mz  at  a  lower  temperature  t^  and  as  soon  as  thermal  equilibrium  is 


SPECIFIC    HEAT.  263 

established  throughout,  the  temperature  of  the  mixture  t  is  taken. 
Let  s  represent  the  specific  heat  of  the  substance  sought.  Then  the 
quantity  of  heat  lost  by  the  substance  is  m  X  s  (t\  —  t)  calories  ; 
while  that  gained  by  the  water  is  m2  (t  —  12)  calories.  Now  if  no 
heat  be  lost  during  the  operation,  m  X  s  (ti  —  t)  =  w2  (t  —  £2),  whence 

s  =  —  ^  •     For  example,  taking  the  quantities  obtained  in  the 

7/1   (C^         Lj 

q  /q  q  _  A\ 

experiment  above,  we  find  for  lead  (300  g=^=.3  K)  s  =    '    )  A* 

.0  (1UU  —  o.oj 

=  .034  calorie. 

223.  /Specific  heat  of  the  same  substances  at  different  tem- 
peratures and  in  the  three  states  of  'matter.  —  The  specific  heat 
of  solids  and  liquids  usually  increases  slightly  with  the  tem- 
perature, and  diminishes  with  increase  of  density.  The  spe- 
cific heat  of  water  at  0°,  40°,  and  80°  is  respectively  1,  1.003, 
and  1.0089  calories.  Substances  in  the  liquid  state  usually 
have  a  higher  specific  heat  than  in  the  solid  or  gaseous  state. 
Thus,  water  has  nearly  double  the  specific  heat  of  ice,  and  a 
little  more  than  double  the  specific  heat  of  steam. 

The  mean  specific  heat  of  a  substance  between  0°  and  t°  is  the 
average  quantity  of  heat  (e.g.  of  calories)  per  degree  required  in 
heating  a  unit  mass  of  the  body  from  0°  to  t°.  Let  h  be  the  total 
number  of  thermal  units  required  to  heat  the  unit  mass  of  the 
substance  from  0°  to  £°,  then  the  mean  specific  heat  s  between  0° 
and  t°  is  expressed  by  the  formula 


The  specific  heat  of  any  perfect  gas  measured  by  its  mass  is 
independent  of  temperature  and  density  ;  for  an  imperfect  gas 
(vapor),  it  increases  with  the  temperature,  and  diminishes  with 
increase  of  density.  The  specific  heat  of  all  perfect  gases  measured 
by  volume  depends  on  the  number  of  atoms  in  the  molecule,  being 
proportional  to  that  number.  Thus  the  specific  heats  of  all  diatomic 
perfect  gases  are  nearly  the  same  ;  that  of  a  triatomic  gas  would  be 
to  these  as  3  :  2,  etc. 


264  MOLECULAR    DYNAMICS. 


REFERENCE  TABLES. 

Table  of  mean  specific  heat  between  0°  C.  and  100°  C. 

fi 


Sulphur      .-' 2026 

Glass 1770 

Iron       .     .£,&* 113 


Copper    .     .  •**CAr    .     .     .     .095 


Mercury       .*.     .     .     -033 


. 


Lead  .  .031 


Specific  heat  of  the  same  substance  in  different  states. 

Solid  Liquid  Gaseous 

Water     .  /?£.  &?    .....  504       .     .     .       1.000       ...       .480 

Bromine    ^  4-  ......  083       ...         .106       ...       .055 

Lead       .    @J$r  .     .     ...     .       .031       .     .     .         .040       ....... 

Alcohol       '£.  tSfer   .........  55-.  77       .     .     .         .45 


224.  Great  capacity  of  ivater  for  heat.  —  Water  requires 
more  heat  to  warm  it,  and  gives  out  more  in  cooling  through 
a  given  range  of  temperature,  than  any  other  substance  except 
hydrogen.     The  quantity  of  heat   that  raises  a  kilogram  of 
water  from  0°  to  100°  C.  would  raise  a  kilogram  of  iron  from 
0°  to  800°  or  900°  0.,   or  above  a  red   heat.     Conversely,  a 
kilogram  of  water  in  cooling  from  100°  to  0°  C.  gives  out  as 
much  heat  as  a  kilogram  of  iron  in  cooling  from  about  900° 
to  0°  C. 

"  The  vast  influence  which  the  ocean  must  exert  as  a 
moderator  of  climate  here  suggests  itself.  The  heat  of 
summer  is  stored  up  in  the  ocean,  and  slowly  given  out 
during  the  winter.  This  is  one  cause  of  the  absence  of 
extremes  in  an  island  climate." 

The  high  specific  heat  of  water  is  utilized  in  heating 
buildings  by  hot  water. 

225.  Relation  between  specific  heat  and  atomic  mass. 

The  heat  energy  of  a  molecule  of  hydrogen  is  equal  to  that  of  a 
molecule  of  oxygen  at  the  same  temperature  ;  and  a  mass  of 
hydrogen  contains  sixteen  times  as  many  molecules  as  an  equal 
mass  of  oxygen.  Hence  a  given  mass  of  hydrogen  possesses  sixteen 


EFFECTS    OF    HEAT.  265 

times  as  much  heat  energy  as  an  equal  mass  of  oxygen  at  the  same 
temperature.  Therefore,  to  produce  a  given  rise  in  the  temperature 
of  a  mass  of  hydrogen,  sixteen  times  as  much  heat  is  required  as 
for  an  equal  mass  of  oxygen  ;  hence  the  specific  heat  or  thermal 
capacity  of  hydrogen  is  sixteen  times  that  of  oxygen. 

226.  Specific  heat  of  elementary  gases  varies  inversely  as 
their  atomic  masses;  or,  the  product  of  the  specific  heat  and 
atomic  mass  is  constant. 

When  the  molecules  are  constrained  by  cohesion,  as  in  liquids 
and  solids,  a  part  of  the  heat  applied  to  a  body  is  spent  in  raising 
its  temperature  and  a  part  in  doing  internal  work  in  overcoming 
cohesion  between  the  molecules  of  the  body  and  in  forcing  them  to 
take  up  new  positions.  The  greater  the  portion  of  heat  consumed, 
i.e.  converted  into  potential  energy,  in  doing  internal  work,  the  less 
there  is  left  to  raise  its  temperature.  Hence  the  law  as  given  for 
gases  holds  only  approximately  for  liquids  and  solids. 


SKCTION  VI. 

EFFECTS    OF    HEAT.       EXPANSION. 

Having  learned  something  of  the  nature  of  heat  and  the 
methods  by  which  it  is  measured,  we  will  next  direct  our 
attention  to  some  effects  it  produces,  viz.  expansion  and 
change  of  state.  The  first,  as  we  have  learned,  furnishes  a 
means  of  measuring  temperature  and  leads  to  a  fuller  study 
of  gases  than  has  yet  been  made.  Under  the  second  effect 
we  study  liquefaction  and  raporization. 

227.  Experiments  illustrating  expansion  of  solids,  liquids. 
and  gases. 

Experiment  1.  — Take  two  brass  tubes,  one  of  a  size  that  will  permit 
it  just  to  enter  the  bore  of  the  other.  Heat  the  smaller  tube  ;  it  will  not 
in  its  expanded  state  enter  the  other.  Thrust  the  heated  tube  into  cold 
water  ;  its  temperature  falls,  and  it  now  enters  the  bore  of  the  other  tube. 
•'  Heat  expands,"  but  "  cold  "  does  not  "  contract. "  Cohesion,  when  a 


266 


MOLECULAR   DYNAMICS. 


diminution  of  heat  (which  acts  as  a  repellent  force)  permits,  causes  a 
solid  or  liquid  body  to  contract.     Cold  is  a  term  of  negation  signifying 
merely  a  greater  or  less  deficiency  of  heat ;  it  is  not  an  entity,  hence  it 
cannot  be  the  direct  cause  of  any  phenomenon. 

Experiment  2.  —  Fig.  204  represents  a  thin  brass  plate  and  an  iron 
plate  of  the  same  dimensions  riveted  together  so  as  to  form  what  is  called 

a  compound  bar.    Place  the  bar  edgewise 
c^^p^Satiii:......: ,:,,,.,  -7—-* . ..  . ,  — r— : al    m  a  flame,  dividing  the  flame  in  halves 

2Q4  (one  half  on  each  side  of  the  bar)  so 

that  both  metals  may  be  equally  heated. 

The  bar,  which  was  at  first  straight,  is  now  bent,  owing  to  the  unequal 
expansion  of  the  two  metals  on  receiving  equal  increments  of  temperature. 


FIG.  205. 


FIG.  20G. 


When  heated  above  the  normal  temperature,  the  brass,  which  is  more 
expansible,  will  be  on  tne  convex  side ;  when  cooled  below  the  normal 
temperature,  it  will  be  on  the  concave  side,  since  it  contracts  more 
rapidly  than  iron. 

Metallic  thermometers  now  in  common  use  (Fig.  205)  are  con- 
structed on  this  principle.  They  contain  a  compound  ribbon  of 
metal  (Fig.  206)  wound  into  a  spiral,  one  end  of  which  a  is  fixed 


EXPANSION-COEFFICIENTS.  267 

so  as  to  be  immovable,  while  the  other  is  attached  to  a  contrivance 
for  multiplying  motion  which  moves  the  index.  With  a  rise  in  tem- 
perature, the  more  expansible  metal  on  the  outside  produces  an 
increase  of  curvature,  which  causes  the  spiral  to  wind  up  closer. 
This  motion  is  communicated  to  the  index,  which  points  on  the 
dial  to  the  corresponding  temperature.  With  a  fall  of  temperature 
the  action  is  reversed. 

Advantage  is  taken  of  this  principle  also  in  the  construction  of 
balance  wheels  of  chronometers.  The  rate  of  vibration  of  a  chro- 
nometer balance  wheel  depends  upon  its  mass 
and  the  distance  of  its  circumference  from  the 
center.  The  parts  BC  and  FG  (Fig.  207)  are 
made  up  of  a  compound  strip,  the  more  expan- 
sible metal  being  on  the  outside.  As  the  tem- 
perature rises  the  radii  A  A  expand,  and  the 
chronometer  would  lose  time,  but  the  heat 
causes  the  strip  BC  and  FG  to  curve  inwards. 
The  masses  D  and  D'  are  thus  brought  nearer  the  center,  and  this 
compensates  for  the  expansion  of  A. 

Experiment  3.  —  Fit  stoppers  tightly  in  the  necks  of  two  similar  thin 
glass  flasks  (or  test-tubes),  and  through  each  stopper  pass  a  glass  tube 
about  60  cm  long.  The  flasks  must  be  as  nearly  alike  as  possible.  Fill 
one  flask  with  alcohol  and  the  other  with  water,  and  crowd  in  the  stop- 
pers so  as  to  force  the  liquids  in  the  tubes  a  little  way  above  the  corks. 
Set  the  two  flasks  into  a  basin  of  hot  water,  and  note  that,  at  the  instant 
the  flasks  enter  the  hot  water,  the  liquids  sink  a  little  in  the  tubes,  but 
quickly  begin  to  rise,  until,  perhaps,  they  reach  the  top  of  the  tubes  and 
run  over. 

When  the  flasks  first  enter  the  hot  water  they  expand,  and  thereby 
their  capacities  are  increased  ;  meantime  the  heat  has  not  reached  the 
liquids  to  cause  them  to  expand,  consequently  the  liquids  sink  momen- 
tarily to  accommodate  themselves  to  the  enlarged  vessel.  Soon  the  heat 
reaches  the  liquids,  and  they  begin  to  expand,  as  shown  by  their  rise  in 
the  tubes.  The  alcohol  rises  faster  than  the  water.  Different  substances, 
in  both  the  solid  and  the  liquid  states,  expand  unequally  on  experiencing 
equal  changes  of  temperature. 

Experiment  4-  — Take  a  dry  flask  like  that  used  in  Exp.  3,  insert 
the  end  of  the  tube  in  a  bottle  of  colored  water  (Fig.  208),  and  apply 
heat  to  the  flask  ;  the  enclosed  air  expands  and  comes  out  through  the 
liquid  in  bubbles.  After  a  few  minutes  withdraw  the  heat,  keeping  the 


268 


MOLECULAR    DYNAMICS. 


end  of  the  tube  in  the  liquid  ;  as  the  air  left  in  the  flask  cools,  its  pressure 
decreases,  and  the  water  is  forced  by  atmospheric  pressure  up  the  tube 
into  the  flask,  and  partially  fills  it, 

Experiment  5.  —  Partly  fill  a  foot-ball  with  cold 
air,  close  the  orifice,  and  place  it  near  a  fire.  The 
air  will  expand  and  distend  the  ball. 

228.  Expansion  -  coefficients.  —  The  ex- 
pansion which  attends  a  rise  of  tempera- 
ture depends  not  only  upon  the  size  of  the 
body,  and  upon  the  number  of  temperature 
degrees  through  which  it  is  heated,  but 
upon  a  quantity  peculiar  to  the  substance 
itself  called  its  expansion-coefficient.  This 
term  is  applied  to  the  increase  of  unit-length 
per  degree  rise  of  temperature. 

Suppose  that  a  rod  of  length  I  at  0°  C.  be 
heated  through  t  degrees,  so  that  its  length 

becomes  /x ;  then,  representing  the  linear  expansion-coefficient 

by  c,  we  have 

7  7 

whence  l±  =  I  (1  -j~  ct). 


FIG.  208. 


It 

The  expression  1  -|-  ct,  called  the  expansion-factor,  is  evi- 
dently the  ratio  of  the  final  to  the  original  length.  Hence 
/!  —  I  (1  -|-  ct)  ;  that  is,  multiplying  the  length  of  a  solid  at 
0°  C.  by  the  expansion  factor  gives  its  length  at  t  degrees 
above  zero.  Conversely,  dividing  its  length  at  t°  by  the 
expansion  factor  gives  its  length  at  0°. 


TABLE    OF    MEAN    COEFFICIENTS   OF   LINEAR 

AND    100°   C. 
Glass  ....     0.0000085     Copper 


Platinum 0.0000085 

Steel 0.000012 

Wrought  iron       .     .     .  0.000012 

Cast  iron 0.000011 

Gold .  0,000015 


Brass  . 
Silver . 
Tin  . 
Lead  . 
Zinc  . 


EXPANSION    BETWEEN    0° 

0.000017 

0.000019 

0.000019 

0.000022 

0.000029 

0.000029 


FORCE    IN    EXPANSION    AND    CONTRACTION.          269 

In  the  expansion  of  fluids  we  have  to  do  only  with  increase 
of  volume,  called  volume  or  cubical  expansion.  A  volume- 
expansion-coefficient  is  the  increase  of  unit  volume  per  degree 
rise  of  temperature.  This  is  approximately  3  c,  or  three  times 
the  linear  expansion-coefficient,  and  may  be  taken  as  such  for 
most  practical  purposes.  Likewise,  the  surface  or  superficial 
expansion-coefficient  is  approximately  2  c. 

Not  only  do  the  expansion-coefficients  of  liquids  and  solids 
vary  with  the  substance,  but  the  coefficient  for  the  same 
substance  varies  with  the  temperature,  being  greater  at  high 
than  at  low  temperatures.  Hence,  in  giving  the  expansion- 
coefficient  of  any  substance  it  is  customary  to  give  the  mean 
coefficient  through  some  definite  range  of  temperature,  as 
from  0°  to  100°  C. 

229.  Force  exerted  in  expansion  and  contraction.  —  The  force 
which  may  be  exerted  by  bodies  in  expanding  or  contracting 
may  be  very  great,  as  shown  by  the  following  rough  calcula- 
tion :  If  an  iron  bar,  1  sq.  in.  in  section,  be  raised  from  0°  C. 
(melting  point  of  ice)  to  500°  C.  (a  dull  red  heat),  its  length, 
if  allowed  to  expand  freely,  will  be  increased  from  1  to  1.006, 
its  expansion-coefficient  being  about  .000012.  Now,  a  force 
of  about  90  tons  is  required  to  stretch  a  bar  of  iron  of 
1  sq.  in.  section  this  amount,  and  this  is  very  nearly  the  force 
that  would  be  necessary  to  prevent  expansion  caused  by  the 
heat.  It  would  require  an  equal  force  to  prevent  contraction^ 
(caused  by  what  ?)  if  the  bar  be  cooled  at  500°. 

Boiler  plates  are  riveted  with  red-hot  rivets,  which,  on 
cooling,  draw  the  plates  together  so  as  to  form  very  tight 
joints.  Tires  are  fitted  on  carriage.-wheels  when  hot,  and,  on 
cooling,  grip  them  with  very  great  force. 

It  is  to  be  observed  that  while  the  force  exerted  in  expan- 
sion and  contraction  is  great,  the  distance  through  which  it 
acts  is  very  small,  and  hence  the  quantity  of  work  performed 
is  not  very  great. 


270  MOLECULAR    DYNAMICS. 

230.  Anomalous  expansion  and  contraction.  —  Water  pre- 
sents a  partial  exception  to  the  general  rule  that  matter 
expands  on  receiving  heat  and  contracts  on  losing  it.  If  a 
quantity  of  water  at  0°  C.,  or  32°  F.,  be  heated,  it  contracts 
as  its  temperature  rises,  until  it  reaches  4°  C.,  or  about  39°  F., 
when  its  volume  is  least,  and  therefore  it  has  its  maximum 
density.  If  heated  beyond  this  temperature  it  expands,  and 
at  about  8°  C.  its  volume  is  the  same  as  at  0°.  On  cooling, 
water  reaches,  its  maximum  density  at  4°  C.,  and  expands  as 
the  temperature  falls  below  that  point. 

Water  is  said  to  have  a  negative  expansion-coefficient  be- 
tween 0°  and  4°  C.,  or  between  32°  and  39.2°  F.  A  few  other 
substances,  such  as  india  rubber  and  iodide  of  lead,  contract 
when  heated,  and  have,  therefore,  negative  coefficients. 


SECTION  VII. 

KINETIC     THEORY     OF     MATTER.         LAWS     OF     GASEOUS     BODIES. 
ABSOLUTE    TEMPERATURE. 

231.  Kinetic  theory  of  matter.  —  In  the  case  of  solids  the 
molecules  are  thought  to  move  in  curved  orbits  the  centers  of 
which  are  fixed.  In  liquids  the  orbits  are  curved ;  but,  as 
shown  in  the  phenomena  of  diffusion  (p.  138),  the  molecules 
.have,  besides  the  oscillating  motion,  a  motion  of  translation. 
The  theory  that  the  molecules  composing  all  bodies  of  matter 
are  in  perpetual  relative  motion  is  called  the  kinetic  theory  of 
matter.  This  theory  claims  that  in  gases  the  molecules  are  so 
far  separated  from  one  another  that  their  motions  are  not 
generally  influenced  by  molecular  attractions.  Hence,  in 
accordance  with  the  first  law  of  motion,  the  molecules  of 
gases  move  in  straight  lines  and  with  uniform  velocity  until 
they  collide  with  one  another  or  strike  against  the  walls  of 
the  containing  vessel,  when,  in  consequence  of  their  elas- 


PRESSURE    OF   A   GAS.    ETC. 


271 


ticity,  they  at  once  rebound  and  start  on  a  new  path.  We 
may  picture  to  ourselves  what  is  going  on  in  a  body  of  calm 
air,  for  instance,  by  observing  a  swarm  of  bees  in  which 
every  individual  bee  is  flying  with  great  velocity,  first  in  one 
direction  and  then  in  another,  while  the  swarm  either  remains 
at  rest  or  sails  slowly  through  the  air. 

232.  Pressure  of  a  gas  due  to  the  kinetic  energy  of  its 
molecules.  —  Consider,  then,  what  a  molecular  storm  must  be 
raging  about  us,  and  how  it  must  beat  against  us  and  against 
every  exposed  surface.  According  to  the  kinetic  theory,  the 
pressure  of  a  gas  (or  its  expansive  force  as  it  is  sometimes 
called)  is  entirely  due  to  the  striking  of  the  molecules  against 
the  surfaces  on  which  the  gas  is  said  to  press,  the  impulses 
following  one  another  in  such  rapid  succession  that  the  effect 
produced  cannot  be  distinguished  from  constant  pressure.1 
Upon  the  kinetic  energy  of  these  blows,  and  upon  the  number 
of  blows  per  second,  must  depend  the  amount  of  pressure. 
But  we  have  learned  that  on  the  energy  of  the  individual 
molecules  depends  that  condition  of  a  gas  called  its  tempera- 
ture; so,  it  is  apparent,  as  stated  above,  that  the  pressure  of  a 
given  quantity  of  gas  varies  with  its  temperature.  Again,  as 
at  the  same  temperature  the  number  of  blows  per  second 
must  depend  upon  the  number  of  molecules  in  the  unit  of 
space,  it  is  apparent  that  the  pressure  varies  with  the  density. 

"If  the  rarefaction  of  air  can  be  carried  so  far  that  only  one 
particle  out  of  every  million  is  left  in  the  space  exhausted,  the  mean 
path  of  the  particles  would  then  be  about  4  inches.  In  our  atmos- 
phere at  a  hight  of  210  miles,  the  particles  are  relatively  so  few 

1  The  following  estimates  made  (by  Maxwell,  using  a  proposition  formulated  by 
Clausius)  for  hydrogen  molecules  at  0°C.,  and  under  a  pressure  of  760mm,  may 
prove  interesting : 

Mean  velocity,  6100  feet  per  second. 

Mean  path  without  collision,  38  ten-million ths  of  an  inch. 

Collisions,  17,750  millions  per  second. 

Mass,  216,000  million  million  million  in  1  gram. 

Number,  19  million  million  million  fill  1  cubic  centimeter. 


272 


MOLECULAR    DYNAMICS. 


"that  each  particle  might  travel  through  a  uniform  atmosphere  of 
that  density  for  sixty  million  miles  without  entering  into  collision." 
—  DANIELL. 

233.    Expansion  and  expansive  force  of  (jases. 

The  effect  of  a  change  of  temperature  upon  a  gas  may  be  meas- 
ured by  noting  the  change  in  its  volume  when  the  pressure  upon 
it  is  constant,  or  the  change  in  its  pressure  when  its  volume  is 
unchanged.  Conversely,  the  changes  in  volume  or  pressure  of  a 


FIG.  209. 

gas  may  be  made  to  indicate  changes  in  temperature.     On  this 
principle  the  so-called  air-thermometer  is  constructed. 

The  relation  between  pressure  and  temperature  of  air  kept  at  a 
constant  volume  may  be  found  by  means  of  an  apparatus  like  that 
represented  in  Fig.  209.  A  bulb  6,  whose  capacity  at  0°  and 
100°  C.  is  known,  is  filled  with  dry  air.  The  capillary  tube  leading 
from  the  bulb  is  connected  to  a  tube  T,  which  is  connected  with 


ABSOLUTE    ZERO.  273 

another  tube  T"  open  to  the  atmosphere.  The  lower  ends  of  T  and 
T'  dip  into  a  reservoir  of  mercury  R.  The  bulb  b  is  first  sur- 
rounded by  melting  ice,  and  by  means  of  the  screw  S  the  mercury 
is  forced  to  the  hight  h  in  the  tube  T,  and  the  difference  in  level 
between  (h  and  h')  the  surfaces  of  mercury  in  the  two  tubes  is 
ascertained.  By  adding  this  to  the  hight  of  the  barometer  at  the 
same  moment,  the  total  pressure  to  which  the  air  in  the  bulb  is 
subjected  at  the  temperature  (0°  C.)  of  melting  ice  is  ascertained. 
The  bulb  is  next  introduced  into  an  apparatus  for  boiling  water,  as 
shown  in  the  figure,  and  surrounded  with  steam  from  the  boiling 
water.  By  means  of  the  screw  S  the  mercury  is  again  forced  to 
the  same  hight  h  as  before  in  the  tube  T.  But  since  the  pressure  of 
air  increases  with  the  temperature,  the  mercury  will  now  be  much 
higher  in  tube  T'  and  higher  in  proportion  to  the  increased  pressure. 
By  this  means  Regnault  ascertained  that  the  pressure  of  dry  air 
confined  to  the  same  volume  is  about  1.367  times  greater  at  100° 
than  at  0°  C.  ;  in  other  words,  the  increase  of  pressure  for  100°  is 
.367,  or  (.367  -f  100  =  )  .00367  per  degree. 

By  a  slight  modification  of  this  instrument  and  a  variation  in  the 
method  of  using  it,  Regnault  ascertained  that  when  air  is  allowed 
to  dilate  with  increase  of  temperature  while  the  pressure  remains 
constant,  the  volume  at  100°  is  increased  by  .367  its  volume  at  0°. 
Dividing  this  number  by  100,  we  obtain  .00367  for  the  expansion 
coefficient  of  air  between  0°  and  100°  C. 

It  is  found  that  the  expansion-coefficient  of  all  gases  is  approxi- 
mately the  same  as  long  as  they  remain  true  gases,  but  as  they 
approach  the  vaporous  state  the  coefficient  changes  rapidly. 

234.  Absolute  zero.  —  The  zeros  on  the  thermometric  scales 
which  we  have  hitherto  considered  are  provisional,  arbitrary. 
Absolute  zero  is  the  temperature  corresponding  to  total 
absence  of  heat.  At  the  absolute  zero  the  molecules  must  be 
supposed  to  be  at  rest.  At  this  temperature  gases  (if  they 
may  be  called  such)  exert  no  pressure,  and  occupy  no  space 
save  that  which  their  molecules  take  up  when  closely  packed 
together.  The  point  of  absolute  zero  is  independent  of  the 
conventions  of  man.  It  is  a  point  of  absolute  cold  or  absence 
of  heat,  beyond  which  no  cooling  is  conceivable. 

Now  it   has  been  found  (§  233)  that  the  pressure  in  air 


274  MOLECULAR    DYNAMICS. 

increases  or  diminishes  by  .00367  =  (about)  ^fa  of  its  pressure 
at  0°  for  each  centigrade  degree  of  rise  or  fall  of  tempera- 
ture, the  volume  being  maintained  constant.  If  air  were  a 
perfect  gas,  and  could  be  cooled  down  in  this  way  to  —  273° 
C.  (—  459.4°  F.),  it  would  exert  no  pressure.  The  reason  it 
would  exert  no  pressure  is  that  its  particles  possess  no  kinetic 
energy,  no  motion.  This  is  assumed,  therefore,  to  be  the 
absolute  zero  of  temperature. 

235.  Thermo-dynamic  definition  of  temperature. 

In  this  system,  temperature,  t,  is  defined  by  the  equation  E  =  kt, 
in  which  E  is  the  average  kinetic  energy  per  molecule  of  a  perfect 
gas  which  has  that  temperature,  and  k  is  a  constant.  This  is  called 
the  thermo-dynamic  definition  of  temperature. 

236.  Absolute  temperature.  —  Absolute  temperature  is  that 
reckoned  from  the  absolute  zero,  or  — 273°  C.     Temperatures 
measured  from  absolute  zero  are  proportional  to  the  pressure  of 
a  theoretically  perfect  gas  of  constant  volume  or  density  /   this 
statement  is  merely  a  convenient  expression  of  the  laws  of  a 
perfect  gas  (§  237). 

The  absolute  temperature  (based  on  the  above  theory)  of 
any  body  is  found  by  adding  273  to  its  temperature  as 
indicated  by  a  centigrade  thermometer,  or  459.4  to  its  tem- 
perature as  indicated  by  a  Fahrenheit  thermometer.  The 
comparative  scale  given  on  p.  257  will  make  this  clear. 

237.  Laws  of  gaseous  masses.  • —  It  follows,  from  the  above 
discussion,  (1)  that  the  volume  of  a  given  mass  of  gas  at  con- 
stant pressure  is  proportional  to  its  absolute  temperature;  i.e.  at 

v  (volume  of  a  given  mass  of  gas) 

constant  pressure  — * — _,  .  ,  -  remains 

T  (absolute  temperature) 

constant.     This  is  called  the  Law  of  Charles. 

(2)  The  pressure  of  a  given  mass  of  gas  whose  volume  is  kept 
constant  is  proportional  to  its  absolute  temperature. 

Boyle's  law  states  that  (3)  at  a  constant  temperature  the 
volume  of  a  given  mass  of  gas  is  inversely  proportional  to  its 


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LAWS    OF    GASEOUS    MASSES.  275 

pressure;  i.e.  the  product  of  its  pressure  and  its  volume  is  con- 
stant. Now,  when  both  the  pressure  and  the  volume  vary  at 
the  same  time,  it  may  be  shown  that  (4)  the  product  of  the 
pressure  and  the  volume  of  a  given  mass  of  gas  is  proportional 
to  its  absolute  temperature.  A  gas  is  said  to  be  perfect,  wheli 
it  perfectly  obeys  these  laws. 

We  may  also  state  this  law  as  follows  :  the  product  of  the 
pressure  and  volume  of  a  given  mass  of  gas  divided  by  its 
absolute  temperature  is  a  constant  quantity,  or 

FV-c 

~Y-  G, 

in  which  P  =  pressure,  V=  volume,  T=  absolute  temperature 
of  a  given  mass  of  gas,  and  C  —  a  constant  quantity,  the  value 
of  which  depends  on  the  gas  in  question. 

Exercises. 

*  1.    Find,  in  both  centigrade  and  Fahrenheit  degrees,  the  absolute  tem- 
peratures at  which  mercury  boils  and  freezes. 

•  2.    At  0°C.   the  volume  of  a  certain  mass  of  gas  under  a  constant 
pressure  is  500  cc  ;   a.   What  will  be  its  volume  if  its  temperature  be 
raised  to  75° C.?    6.  What  will  be  its  volume  if  its  temperature  become 
—  20°  C.? 

*3.  If  the  volume  of  a  mass  of  gas  at  20°  C.  be  200  cc,  what  will  be  its 
volume  at  30° C.?  Solution:  20° C.  is  equivalent  to  (20  +  273)  293  abs. 
temp.  ;  then  293  :  303  :  :  200  :  206.8  cc.  Ans. 

4.  To  what  volume  will  a  liter  of  gas  contract  if  cooled  from  30°  C.  to 
-15°C.? 

.  ;">.  One  liter  of  gas  under  a  pressure  of  one  atmosphere  will  have  what 
volume,  if  the  pressure  be  reduced  to  900  g  per  square  centimeter,  while 
the  temperature  remains  constant  ? 

6.  The  volume  of  a  certain  mass  of  air  at  a  temperature  of  17° C., 
under  a  pressure  of  800  g  per  square  centimeter,  is  500  cc  ;  what  will  be 
its  volume  at  a  temperature  of  27°C.,  under  a  pressure  of   1200  g  per 
square  centimeter?  •  Solution:  17° C.  is  equivalent  to  290°  abs.  temp.  ; 
27°  C.  is  equivalent  to  300°  abs.  temp.     Then  290  :  300  :  :  500  X  800  :  x  x 
1200.     Whence  x  =  344.8  cc.     Ans. 

7.  If  the  volume  of  a  mass  of  gas  under  a  pressure  of  1  K  per  square 


276  MOLECULAR    DYNAMICS. 

centimeter  at  a  temperature  of  0°C.  be  1  liter,  at  what  temperature  will 
its  volume  be  reduced  to  1  cc  under  a  pressure  of  200  K  per  square  centi- 
meter ?  Ans. :  54.6°  abs.  temp.,  or  —  218.4° C. 

*  8.    Find  the  temperatures  on  the  absolute  scale  at  which  the  substances 
named  on  p.  278  melt. 

•  9.    If  a  cubic  foot  of  coal-gas  at  32°  F. ,  when  the  barometer  is  at  30  in. , 
has  a  mass  of  ^  lb.,  what  will  be  the  mass  of  an  equal  volume  at  68°  F., 
when  the  barometer  is  at  29  in.  ? 

10.  Explain  the  following  statement :  ' '  To  compare  absolute  tem- 
peratures, we  may  seal  up  a  mercurial  barometer  in  a  tube,  or  an  aneroid 
barometer  in  a  preserving  jar."  WHITING. 


SECTION  VIII. 

EFFECTS    OF    HEAT.       FUSION. 

238.  Change  of  properties  in  solids  attending  change  of  tem- 
perature. —  "  Every  known  -property  of  a  piece  of  matter, 
except  its  mass,  varies  with  variation  of  temperature."     Inas- 
much as   heat   tends    to  weaken  cohesion,  the  rigidity  and 
tenacity  of  solids  are  generally  lessened,  and  their  plasticity 
is  increased,  by  the  addition  of  heat. 

239.  Fusion.  —  As  previously  stated,  whether  a  given  sub- 
stance exist  in  a  solid,  liquid,  or  gaseous  state  depends  upon 
the  temperature  and  the  pressure  it  is  under.     Solids  exposed 
to  heat  liquefy  or  fuse,  unless  previously  decomposed.    Some, 
like  ice  and  tin,   change  their  state  abruptly ;   others,  like 
glass  and  wrought  iron,  become  plastic  prior  to  liquefaction. 
The  temperature   at  which  a  substance  melts  is  called  its 
fusion-point.     The  fusion-points  of  different  substances  vary 
greatly  :   that  of  alcohol  (— 130.5°  0.)   and  that  of  iridium 
(1950°  C.)  may  be  taken  as  extreme  examples. 

Experiment  and  experience  teach  that  (1)  the  melting  or 
solidifying  point  (they  are  approximately  the  same  for  the  same 
substance)  may  vary  widely  for  different  substances,  but  for  the 
same  substance  it  is  invariable  when  under  the  same  pressure. 


CHANGE    OF    VOLUME    DURING    SOLIDIFICATION.     277 

(2)  The  temperature  of  a  solid  or  liquid  remains  constant  at 
the  melting-point  from  the  moment  that  melting  or  solidification 
begins  until  it  ceases. 

Experiment  1.  —  Put  a  lump  of  ice  as  large  as  your  two  fists  into 
boiling  water ;  when  it  is  reduced  to  about  i  its  original  size,  skini  it  out. 
Wipe  the  lump,  and  place  one  hand  on  it  and  the  other  on  a  lump  to 
which  heat  has  not  been  applied  ;  you  will  not  perceive  any  difference  in 
their  temperatures.  Under  ordinary  pressure  ice  cannot  be  made  warmer 
than  0°  C. 

240.  Change  of  volume  during  fusion  or  solidification. 
During  these  changes  of  state  there  is  usually  a  change  of  volume. 

Generally  solids  expand  on  melting,  so  that  the  volume  is  increased 
and  the  density  is  diminished  by  fusion.  There  are,  however, 
certain  important  exceptions  to  this  rule.  Ice  and  type-metal,  for 
example,  float  in  the  denser  liquids  of  these  substances  respectively. 
Such  metals  as  expand  on  solidifying  are  especially  adapted  for 
casting,  since  they  expand  and  fill  every  portion  of  the  mould,  and 
the  resulting  impression  is  sharp  and  clear. 

241.  Effect  of  pressure  on  the  fusion  point. 

In  solids  whose  volume  increases  during  fusion,  the  fusion  is  more 
difficult  when  the  pressure  is  increased,  since  not  only  is  heat 
required  to  change  the  state  of  the  body,  but  an  additional  quantity 
is  required  to  do  additional  external  work  against  the  additional 
pressure.  In  solids  whose  volume  decreases  during  fusion,  an 
increase  of  pressure  facilitates  the  fusion,  and  the  temperature  is 
less  as  the  pressure  is  greater.  Briefly,  then,  pressure  lowers  the 
fusion  point  of  substances  that  expand  on  solidifying,  and  raises  the 
fusion  point  of  those  that  contract. 

242.  Hegelation. 

Experiment  2.  —  Place  in  contact  the  smooth  surfaces  (wiped 
dry)  of  two  pieces  of  ice ;  press  them  together  for  a  few  seconds  ; 
remove  the  pressure,  and  they  will  be  found  to  be  firmly  frozen 
together. 

This  phenomenon  is  called  regelation,  and  is  simply  the  con- 
sequence of  lowering  the  fusion  point  by  pressure.  The  fusion 
point  being  lowered,  the  ice  at  the  surfaces  of  contact  is  melted,  but 
as  the  water  produced  is  below  the  normal  fusion  point  of  water,  it 
freezes  again  as  soon  as  the  pressure  is  removed. 


278 


MOLECULAR    DYNAMICS. 


TABLE  OF  FUSION  POINTS. 

Alcohol  ^l^j^-H^  —  130.5°  C. 

Zinc  .     ...     .  about  .     .  425°  C. 

Mercury  .    Wh 

°P's*   ~38'8° 

Silver     .     .     .       " 

.     .  954° 

Sulphuric  acid,  J 

.     .     -34.4° 

Gold.     . 

.      1200° 

Ice  .     .     .     .ft 

jM    o° 

Cast  iron    .    '.'£-  " 

1050-1250° 

Phosphorus  .AF 

.     .            44° 

Wrought  iron  .  ^2j.' 

1500-1600° 

Sulphur    .,;•*>  . 

.     .          115° 

Platinum    .            " 

.      1775° 

Tin       . 
Lead    .     .$L 

.  about  233° 
"      334° 

Iridium  (the  most 
infusible  rnetaD  " 

1950° 

243.  Heat  of  fusion.  —  The  temperature  of  ice  remains 
constant  while  melting,  and  generally  heat  imparted  to  a 
melting  body  affects  its  temperature  very  little  if  any. 
Furthermore,  ice  and  other  solids  are  not  instantly  converted 
into  liquids  on  reaching  the  fusion  point,  but  absorb  a  quan- 
tity of  heat  proportionate  to  their  mass  before  fusion  is 
accomplished.  Inasmuch  as  none  of  the  heat  applied  during 
melting  raises  the  temperature  of  the  body,  the  question 
arises  what  becomes  of  the  heat  applied  to  the  body?  The 
thermo-dynamical  theory  furnishes  the  only  satisfactory 
answer  to  this  important  question.  The  answer  is,  about  all 
the  heat  applied  to  a  body  during  fusion  is  consumed  in  doing 
internal  work,  as  it  is  called.  The  molecules  that  were  held 
firmly  in  their  places  by  molecular  forces  are,  during  fusion, 
moved  from  their  places,  and  so  work  is  done  against  these 
forces.  Heat,  the  energy  of  motion,  performs  this  work,  and 
is  thereby  converted  into  potential  energy,  the  energy  of 
position,  —  energy  of  the  same  kind  as  that  of  a  raised 
weight.  The  heat  which  disappears  in  melting  is  called  the 
heat  of  fusion. 

If  it  require  a  large  quantity  of  heat  and  a  long  time  to 
effect  the  fusion  of  a  body,  it  must  be  inferred  that  the 
amount  of  work  done  is  proportionately  great.  Fortunate  is 
it  that  it  does  require  much  heat  to  melt  moderately  small 


MEASUREMENT   OF   THE   HEAT   OF   FUSION.          279 

masses  of  ice  and  snow,  else  on  a  single  warm  day  in  winter 
all  the  ice  and  snow  would  melt,  creating  most  destructive 
freshets. 

244.  Measurement  of  the  heat  affusion.  —  Let  it  be  required 
to  find  approximately  the  quantity  of  heat  that  disappears 
during  the  melting  of  one  kilogram  of  ice.  This  quantity  is 
most  readily  determined  by  the  method  of  mixtures. 

Experiment  3.  —  Weigh  out  200  g  of  dry  ice  chips  (dry  them  with  a 
towel),  whose  temperature  in  a  room  of  ordinary  temperature  may  be 
safely  assumed  to  be  0°C.  Weigh  out  200  g  of  boiling  water,  whose 
temperature  we  assume  to  be  100°  C.  Pour  the  hot  water  upon  the  ice, 
and  stir  it  until  the  ice  is  all  melted.  Test  the  temperature  of  the  resulting 
liquid. 

Suppose  its  temperature  is  found  to  be  10°  C.  It  is  evident  that  the 
temperature  of  the  hot  water  in  falling  from  100°  to  90°  would  yield 
sufficient  heat  to  raise  an  equal  mass  of  water  from  0°  to  10°  C.  Hence 
it  is  clear  that  the  heat  which  the  water  at  90°  yields  in  falling  from  90° 
to  10°  —  a  fall  of  80°  —  in  some  manner  disappears.  At  this  rate  had  you 
used  1  k  of  ice  and  1  k  of  hot  water,  the  amount  of  heat  lost  would  be  80 
calories.  Careful  experiments,  in  which  suitable  allowances1  are  made 
for  loss  or  gain  of  heat  by  radiation,  conduction,  absorption  by  the  calo- 
rimeter, etc.,  have  determined  that  SO  calories  of  heat  are  consumed  in 
melting  1  kilogram  of  ice. 

TABLE2  or   HEATS  OF  FUSION  OF   SUBSTANCES   UNDER  THE   PRESSURE 
OF  ONE  ATMOSPHERE. 

Calories  Calories  Calories 

per  kilogram.  .  per  kilogram.  per  kilogram. 

Water    ....     80.0        Silver       .  .     24.7         Sulphur  .     .     9.4 

Sodium  nitrate    .     63.0        Tin      .     .  .     14.25      Lead  ...     5.4 

Potassium  nitrate    47.4        Bismuth  .  .     12.6        Phosphorus .     5.0 

Zinc.     ....     28.1         Iodine     .  .     11.7         Mercury.     .     2.82 

According  to  this  table  it  is  to  be  understood,  for  example, 

1  As  this  is  not  a  manual  of  manipulation,  the  cumbersome  details  relating  to 
cautions  against  errors  which  must  be  observed  in  order  to  secure  even  approximately 
accurate  results  are  omitted.    The  student  will  find  ample  directions  in  almost  all  of 
the  many  laboratory  manuals  extant. 

2  Barker. 


280  MOLECULAR    DYNAMICS. 

that  one  kilogram  of  ice  at  0°  under  the  pressure  of  one 
atmosphere,  while  changing  to  a  liquid,  absorbs  without  any 
change  of  temperature  80  calories  of  heat,  or  as  much  heat  as 
is  required  to  raise  80  kilograms  of  water  from  0°  to  1°  C. 
It  will  be  seen  that  water  possesses  the  greatest  latent  heat 
of  fusion. 

245.  Transformation  of  heat  reversible.  —  As  stated  at  the 
beginning  of  this  chapter,  work  is  transformable  into  heat, 
and,  as  stated  on  p.  87,  potential  energy  is  transformed  into 
kinetic  energy  "  by  the  return  of  the  molecules  to  their  orig- 
inal positions  ; "  so  when  water  freezes  or  any  liquid  is 
re-solidified,  the  potential  energy  (latent  heat  of  fusion)  reap- 
pears as  heat. 

Water  in  freezing  undergoes  no  change  of  temperature, 
hence,  if  heat  be  developed  during  the  operation,  it  must 
become  diffused  or  must  be  "  given  off  "  in  order  to  allow  the 
freezing  to  go  on.  As  the  diffusion  is  necessarily  slow,  so 
freezing  must  be  slow  ;  and  this  slow  development  of  heat 
and  its  immediate  dispersion  accounts  for  the  fact  that  we 
are  seldom  made  conscious  of  the  development  of  heat  during 
solidification. 

Farmers  sometimes  turn  to  practical  use  this  well-known 
phenomenon.  Anticipating  a  cold  night,  they  carry  tubs  of 
water  into  cellars  to  be  frozen.  The  heat  generated  thereby, 
although  of  a  low  temperature,  is  sufficient  to  protect  vege- 
tables which  freeze  at  a  lower  temperature  than  water. 

Heat  disappears  in  the  process  of  melting  ice ;  and,  para- 
doxical as  it  may  seem,  heat  is  generated  by  freezing  water. 
By  freezing  one  kilogram  of  water  80  calories  of  heat  are 
generated. 


VAPORIZATION.  281 


SECTION  IX. 

EFFECTS    OF    HEAT    CONTINUED.       VAPORIZATION. 

246.  Evaporation;  ebullition.  —  The  process  of  converting 
a  liquid  into  a  vapor  is  called  vaporization.     A  comparatively 
slow  vaporization  which  takes  place  only  at  the  exposed  sur- 
face of  a  liquid  is  called  evaporation.     A  rapid  process  which 
may  take  place  throughout  the  liquid,  but  usually  is  most 
rapid  at  the  point  where  heat  is  applied,  is  called  boiling  or 
ebullition. 

247.  Kinetic    theory   of    evaporation    and   condensation.  - 
According  to  this  theory,  some  of  the  molecules  in  any  liquid 
move  faster  than  others.     Those  at  the  surface  which  have 
great  velocities,  if  the  direction  of  their  motion  be  from  the 
liquid,  will  break  away  from  the  forces  that  are  able  to  retain 
the   molecules  moving  more    slowly,   and  will  fly  about  as 
vapor  in  the  space  outside  the  liquid.     This  is  evaporation. 
At  the  same  time  molecules  of  the  vapor  striking  the  liquid 
may  plunge  into  it  and   become   entangled  in  it,  and  thus 
there  is  a  return  to  the  liquid  state.     This  is  condensation. 
The  number  of  molecules  which  passes  from  the  liquid  to  the 
vapor  increases  with  increase   of  temperature  of  the  liquid. 
The  number  which  passes   from  the  vapor  to  the  liquid  de- 
pends upon  the  density  of  the  vapor  as  well  as  its  tempera- 
ture.    When  the  density  of  the  vapor  increases  to  such  an 
extent  that  as  many  molecules  are  condensed  as  are  evaporated, 
then  the  vapor  is  said  to  have   its  maximum  density  for  that 
temperature,  or  to  be   saturated.      The  evaporation  then  ap- 
pears to  cease,  because  the  proportions  of  liquid  and  vapor 
remain   unchanged.       Liquids    which    evaporate    readily   are 
called  volatile   liquids  in  distinction  from  those  which  do  not, 
and  which  are  called  fixed  liquids. 

248.  Boiling  point.  —  In   evaporation,  molecules  fly   from 


282 


MOLECULAR    DYNAMICS. 


the  surface  of  the  liquid  and  mingle  with  the  particles  of  the 
air  and  drive  only  a  certain  small  portion  of  them  away.  In 
boiling,  the  molecules  which  fly  away  from  the  surface  drive 
all  the  air  particles  away  a  certain  distance.  Hence  the 
vapor  of  a  boiling  liquid  must  exert  a  pressure  at  least 
as  great  as  the  atmospheric  pressure.  The  greater  the 
external  pressure  to  be  overcome,  the  greater  must  be  the 
energy,  i.e.  the  higher  the  temperature,  of  the  vapor.  When 
the  saturated  vapor  of  a  liquid  exerts  a  pressure  equal  to  that 
of  the  atmosphere,  the  liquid  begins  to  boil,  and  the  tempera- 
ture at  which  this  occurs  is  called  the  normal  boiling  point  of 
that  liquid. 

Experiment  1.  —  Half  fill  a  glass  flask  with  water.  Boil  the  water 
over  a  Bunsen  burner ;  the  steam  will  drive  the  air  from  the  flask.  With- 
draw the  burner,  quickly  cork  the  flask  very  tightly,  and  plunge  the  flask 

into  cold  water,  or  invert  the  flask  and 
pour  cold  water  upon  the  part  contain- 
ing steam,  as  in  Fig.  210  ;  the  water  in 
the  flask,  though  cooled  several  degrees 
below  the  usual  boiling  point,  boils  again 
violently.  The  application  of  cold  wa- 
ter to  the  flask  condenses  some  of  the 
steam,  and  diminishes  the  pressure  of 
the  rest,  so  that  the  pressure  upon  the 
water  is  diminished,  and  the  water  boils 
at  a  reduced  temperature. 

If  hot  water  be  poured  upon 
the  flask,  the  water  ceases  to  boil. 
Under  the  receiver  of  an  air-pump, 
water  may  be  made  to  boil  at 
any  temperature  between  0°  and 
100°  C.  ;  indeed,  if  exhaustion  be 

carried  far  enough,  boiling  and  freezing  may  be  going  on  at  the 
same  time.  When  high  temperature  is  objectionable,  appara- 
tus is  contrived  for  boiling  and  evaporating  in  a  vacuum ;  as, 


BOILING    POINT.  283 

for  instance,  in  the  vacuum  pans  used  in  sugar  refineries.  As 
water  boils  more  easily  under  diminished  pressure,  so  it  boils 
with  more  difficulty  when  the  pressure  is  increased ;  and  the 
temperature  to  which  water  may  be  raised  under  the  pressure 
of  its  own  steam  is  limited  only  by  the  strength  of  the  vessel 
containing  it.  Vessels  adapted  to  resisting  steam  pressure, 
called  digesters,  are  often  employed  to  effect  a  complete  pene- 
tration of  water  into  solid  and  hard  substances.  By  this 
means  gelatine  is  extracted  from  the  interior  of  bones.  In 
the  boiler  of  a  locomotive,  where  the  pressure  is  sometimes 
150  Ibs.  above  the  atmosphere,  the  boiling  point  rises  to  about 
185°  C.  (365°  F.). 

Experiment  2.  —Place  a  test  tube  (Fig.  211)  half  filled  with  ether  in  a 
beaker  containing  water  at  a  temperature  of  60°  C.     Although  the  tem- 
perature of  the  water  is  40°  below  its  boiling  point,  it  very 
quickly  raises  the  temperature  of  the  ether  sufficiently  to 
cause  it  to  boil  violently.     Introduce  a  chemical  thermom- 
eter into  the  test  tube,  and  ascertain  the  boiling  point  of 
ether. 

Experiment  3.  —  In  a  beaker  half  full  of  distilled  water 
suspend  a  thermometer  so  that  the  bulb  will  be  covered  by 
the  water  and  yet  be  at  least  two  inches  above  the  bottom        FlG  211 
of  the  beaker.     Apply  heat  to  the  beaker,  and  observe  any 
changes  of  temperature  which  may  occur,  both  before  and  after  boiling 
begins. 

Experiment  4.  —  Dissolve  table-salt  in  water,  and  you  may  raise  its 
boiling  point  till  it  reaches  108°  C.  With  saltpetre  it  may  reach  115°  C. 

It  is  found  that  (1)  for  a  given  pressure  (for  example,  that 
of  the  atmosphere  at  760  mm)  every  liquid  has  a  definite  boil- 
ing point :  (2)  this  boiling  point  remains  constant  after  boiling 
has  begun;  (3)  salts  dissolved  in  liquids  raise  their  boiling 
points.!  but  do  not  affect  the  temperature  of  the  escaping  vapor. 
The  latter  result  is  obviously  due  to  the  additional  work 
required  to  be  performed  by  the  heat  in  order  to  overcome 
the  increased  cohesion  due  to  the  salt  in  solution. 


284  MOLECULAR    DYNAMICS. 


BOILING  POINTS  UNDER  A  PRESSURE  OF  760  MM. 


'OINTS  i 

1ft- 


Sulphurous  anhydride  *4  V*V—  8°  C. 
Ether      .     .     .     •     •  A-       ^4.89° 
Carbon  disulphide  CL/4^      46. 8° 
Bromine      .    (8-\  .     .       63° 
Wood-spirit    .j   .^.,L       65.50° 


Alcohol  .WJT/UKr         78.39° 


Benzole       ,  .     .     .     .       80.44°  C. 


Water,    r*.  100° 

Acetic  acid  / 

Butyric  acid  , 

Sulphuric  acid  l*  ^337.77 


Mercury  .  .     .358° 


Atmospheres. 

96.  9°  C. 

1.     .     . 

.     .     100°  C. 

97.7° 

2 

.     .     120.6° 

98.5° 

3.     .     . 

.     .     134° 

99.26° 

5  . 

.     .     152.2° 

100° 

10.     .. 

.     .      ISO.  3° 

100.3° 

BOILING  POINTS  OF  WATER  AT  DIFFERENT  PRESSURES 
Barometer. 
680mm  .     .     . 
700    "... 
720    "... 
740    "... 
760    "... 
770    "... 

The  boiling  point  of  water  varies  with  the  altitude  of 
places,  in  consequence  of  the  change  in  atmospheric  pressure. 
Roughly  speaking,  a  difference  of  altitude  of  533  ft.  causes  a 
variation  of  1°  F.  in  the  boiling  point.  The  measurement  of 
hights  by  means  of  the  boiling  point  is  called  hypsometry. 
A  hypsometer  is  simply  a  convenient  portable  apparatus  for 
boiling  water,  provided  with  a  thermometer  sensitive  to  (say) 
0.01°. 

BOILING   POINTS  OF  WATER  AT  DIFFERENT  ALTITUDES. 

Above  the  Mean  hight  of 

sea-level.  Barometer.  Temperature. 

Quito +9,500  ft.  .     .     .  21.53  in.  .     .     .     91°  C. 

Mont  Blanc     .     .     .     15,650  "    .     .     .  16.90  "    .     .     .     86° 

Mt.  Washington .     .       6,290  "...  22.90  "...     94° 

Boston 0  "...  30.00  "...   100° 

Dead  Sea  (below)     .-1,316"    .     .     .  31.50"    .     .     .101° 

249.  Vaporization  of  solids. — The  boiling  point  of  a  sub- 
stance under  ordinary  atmospheric  pressure  may  be  below  its 
fusion  point ;  if  so,  the  solid  changes  directly  into  a  vapor 
without  passing  through  the  usual  intermediate  liquid  state. 
For  example,  the  maximum  vapor  pressure  of  carbon  dioxide 


HEAT    OF    VAPORIZATION. 


285 


at  its  fusion  point  ( — 65°  C.)  is  three  atmospheres  ;  under 
any  less  pressure  it  vaporizes,  but  never  melts.  Ice  cannot  be 
melted  under  less  than  4.6  mm  pressure.  It  requires  a  greater 
pressure  than  that  of  a  single  atmosphere  to  melt  arsenic  and 
arsenious  oxide.  All  of  the  substances  named  above  evapor- 
ate far  below  their  fusion  points.  Hence,  arsenious  oxide  ex- 
posed in  a  room,  in  wall  paper,  for  example,  may  render  the 
air  of  the  room  dangerous  for  inhalation.  Ice  evaporates  at 
temperatures  far  below  the  fusion  point.  Housekeepers  well 
know  that  clothes  dry  without  thawing,  and  it  is  a  familiar 
fact  that  snow-banks  diminish  in  size  when  the  weather  is 
below  zero. 

250.  Heat  of  vaporization.  —  Heat  that  is  consumed  in  the 
process  of  vaporization  is  called  the  heat  of  vaporization. 
The  quantity  of  heat  required  to  convert  a  gram  of  water  at 
100°  C.  into  steam  without  altering  its  temperature  (which  is 
the  same  as  the  quantity  of  heat  generated  by  the  condensa- 
tion of  one  gram  of  steam  at  100°)  is  called  the  heat  of 
vaporization  of  water. 

Experiment  5.  —  Let  it  be  required  to  find  the  heat  of  vaporization  of 
water.  Find  the  mass  in  grams  of  the  glass  beaker  or  calorimeter  C  (Fig.  212), 
and  since  it  will  receive  a  small 
portion  of  the  heat  generated 
by  the  condensation  of  the 
steam,  find  its  water  equiva- 
lent by  multiplying  its  mass 
by  the  specific  heat  of  glass 
(.177).  Represent  this  quan- 
tity by  mi.  Take  in  the 
calorimeter  a  certain  known 
mass  M  of  cold  water  at 
a  known  temperature  t. 
When  water  in  the  flask  A 
begins  to  boil,  introduce  the  FlG>  212" 

end  of  the  delivery  tube  B  into  the  water  in  C.  The  steam  that  passes 
through  the  tube  is  condensed  on  entering  the  cold  water,  and  heats  the 


286  MOLECULAR    DYNAMICS. 

water.  When  a  considerable  portion  of  the  water  in  A  has  been 
vaporized,  the  temperature  ti  of  the  water  in  C  is  taken  again,  and  the 
contents  of  the  calorimeter  are  again  weighed.  The  increase  m  in  the 
mass  of  water  in  C  is  the  mass  of  steam  which  has  been  condensed. 
Let  L  be  the  heat  of  vaporization.  Then  the  whole  quantity  of  heat 
generated  by  the  condensation  of  m  grams  of  steam  is  Lm  and  the  quan- 
tity of  heat  imparted  to  the  cold  water  in  falling  from  100°  to  ti°  is 
m  (100  —  ii),  or  the  total  quantity  of  heat  given  to  the  calorimeter  and  its 
original  contents  is  Lm  +  m  (100  —  ti).  The  heat  required  to  raise  the 
calorimeter  and  its  original  contents  from  t  to  t\  is  (M  +  MI)  (ti  —t). 
But  these  two  quantities  are  equal,  hence 

Lm  +  m  (100  —  ti)  =  (M  +  mi)  (ti  —  t); 

whence  L  =  (M  +  mi}  (tl~t}  ~  m  (1°°  ~  *l}. 
m 

In  practice  various  precautions,  which  need  not  here  be 
detailed,  are  necessary.  Careful  experiments  have  determined 
the  value  of  L  for  steam  to  be  536  (Kohlrausch)  small 
calories  ;  that  is,  it  requires  536  small  calories  of  heat  to 
convert  one  gram  of  water  at  100°  into  steam  at  100°,  or 
536  calories  per  kilogram,  and  when  the  process  is  reversed 
536  calories  per  kilogram  of  steam  are  generated  by  the 
condensation. 

When  water  is  converted  into  steam,  the  larger  portion  of 
the  heat  which  disappears  is  consumed  in  separating  the 
molecules  so  far  that  molecular  attraction  is  no  longer  sen- 
sible ;  a  small  portion  —  about  ^  —  is  consumed  in  over- 
coming atmospheric  pressure.1  The  amount  of  work  done  in 
boiling  is  very  great,  as  shown  by  the  amount  of  heat 
consumed.  Hence  it  requires  a  long  time  for  the  water  to 

1  In  this  connection  a  brief  discussion  of  some  molecular  hypotheses  may  prove  of 
interest.  The  molecule  is  regarded  as  a  collection  of  atoms.  It  may  possess  both 
translatory  and  rotary  motion  as  a  whole,  and  hence  kinetic  energy.  It  may  possess 
potential  energy,  in  virtue  of  the  mutual  attraction  between  it  and  other  molecules 
and  their  relative  distances,  since  the  potential  energy  increases  with  both  the  force 
and  the  distance  apart.  This  latter  may  be  termed  inter-molecular  energy.  The 
atoms  within  the  individual  molecule  may  also  possess  all  these  kinds  of  motion  and 
energy,  and  the  total  amount  of  this  energy  within  the  molecule  may  be  called  infra- 
molecular  energy.  The  work  which  is  performed  when  either  the  inter-  or  intra- 


DISTILLATION. 


287 


acquire  the  requisite  amount  of  heat.  This  is  a  protection 
against  sudden  changes. 

Steam  is  a  most  convenient  vehicle  for  the  conveyance  of 
heat  of  vaporization,  i.e.  potential  energy,  from  the  boiler  to 
distant  rooms  requiring  to  be  heated.  For  example,  for  every 
kilogram  of  steam  condensed  in  the  pipes  of  the  radiator, 
536  calories,  or  heat  enough  to  raise  5.36  kilograms  (about 
12  Ibs.)  of  ice-water  to  the  boiling  point,  are  generated. 

251.    Distillation. 

Experiment  6.  —  Vessel  A  (Fig.  213),  called  a  condenser,  contains  a 
coil  B,  called  a  worm,  of  copper  tubing,  terminating  at  one  extremity  at  a. 
The  other  end  of  the 
tube,  6,  projects  through  d  \ 

the  side  of  the  vessel 
near  its  bottom.  Near 
the  top  of  the  vessel  pro- 
jects another  tube,  c, 
called  the  overflow,  with 
which  is  connected  a 
rubber  tube,  e.  This 
tube  conveys  the  warm 
water  which  rises  from 
the  surface  of  the  heated 
worm  away  to  a  sink  or 
other  convenient  recep- 
tacle. 

Take  a  glass  flask  of 
a  quart  capacity,  fill  it 
three  -  fourths  full  of 
pond  or  bog  water.  Connect  the  flask  by  means  of  a  glass  delivery-tube 


FIG.  213. 


molecular  energy  is  altered,  or  both  are  altered,  is  called  disgregation  work.  The 
heat  energy  is  regarded  as  the  kinetic  energy  of  the  molecules  in  their  vibratory 
motions,  apart  from  any  energy  of  rotation  about  their  own  centers  of  mass,  and 
apart  from  inter-  or  intra-molecular  energy. 

"When  heat  is  imparted  to  a  body,  it  is  distributed,  in  general,  so  as  to  produce,  in 
varying  relative  quantities,  four  effects,  viz.  :  (1)  to  raise  the  temperature  by 
increasing  the  vibratory  speed  of  the  molecular  motion  ;  (2)  to  perform  external 
work ;  (3)  to  perform  inter-molecular  work  ;  (4)  to  perform  intra-molecular  work. 
3  and  4  are  classed  as  disgregation  work. 


288  MOLECULAR    DYNAMICS. 

with  the  extremity  a  of  the  worm.  Heat  the  water  in  the  flask  ;  as  soon 
as  it  begins  to  boil,  commence  siphoning  cold  water  through  a  small  tube,  d, 
from  an  elevated  vessel,  E,  into  the  condenser.  Inasmuch  as  the  worm  is 
constantly  surrounded  with  cold  water,  the  steam  on  passing  through  it 
becomes  condensed  into  a  liquid,  and  the  liquid  (called  the  distillate) 
trickles  from  the  extremity  b  into  a  receiving  vessel.  The  distillate  is 
clear,  but  the  water  in  the  flask  acquires  a  yellowish  brown  tinge  as  the 
boiling  progresses,  due  to  the  concentration  of  impurities  (largely  of 
vegetable  matter)  which  are  held  in  suspension  and  solution  in  ordinary 
pond  water.  The  apparatus  used  is  called  a  still,  and  the  operation 
distillation. 

When  a  volatile  liquid  is  to  be  separated  from  water,  —  for 
example,  when  alcohol  is  separated  from  the  vinous  mash  after 
fermentation,  —  the  mixed  liquid  is  heated .  to  its  boiling- 
point,  which  is  lower  than  that  of  water.  Much  more  of  the 
volatile  liquid  will  be  converted  into  vapor  than  of  the  water, 
because  its  boiling  point  is  lower.  Thus  a  partial  separation 
is  effected.  By  repeated  distillations  of  the  distillate,  a  95 
per  cent  alcohol  is  obtained. 


SECTION  X. 

METHODS    OF    PRODUCING    COLD    ARTIFICIALLY. 

A  body  becomes  cold  only  by  losing  heat.  As  heat  passes 
only  from  warmer  to  colder  bodies,  it  is  evident  that  the 
temperature  of  a  body  cannot  fall  below  that  of  surrounding 
bodies,  —  for  example,  below  the  temperature  of  other  bodies 
in  the  same  room,  —  by  the  natural  process  of  imparting  heat 
to  its  neighbors.  The  temperature  of  a  body,  then,  can  be 
reduced  below  that  of  its  neighbors  only  by  some  artificial 
means. 

The  fact  that  heat  must  be  consumed  in  the  conversion 
of  solids  into  liquids  and  liquids  into  vapors,  because  work  is 
done,  is  turned  to  practical  use  in  many  ways  for  the 


HEAT    CONSUMED    IN    EVAPORATION.  289 

purpose  of  producing  artificial  cold.     The   following  experi- 
ments will  illustrate  this  process. 

252.  Heat  consumed  in  dissolving.  —  Freezing  mixtures. 

Experiment  1.  —  Prepare  a  mixture  of  2  parts,  by  mass,  of  pulverized 
ammonium  nitrate  and  1  part  of  ammonium  chloride.  Take  about  75  cc 
of  water  (not  warmer  than  8°C.),  and  into  it  pour  a  large  quantity  of  the 
mixture,  stirring  it  while  dissolving  with  a  test-tube  containing  a  little 
cold  water.  The  water  in  the  test-tube  will  be  quickly  frozen.  A  finger 
placed  in  the  solution  will  feel  a  painful  sensation  of  cold,  and  a  thermom- 
eter will  indicate  a  temperature  of  about  —  10°  C. 

One  of  the  most  common  freezing  mixtures  consists  of 
3  parts  of  snow  or  broken  ice  and  1  part  of  common  salt. 
The  affinity  of  salt  for  water  tends  to  produce  liquefaction  of 
the  ice,  and  the  resulting  liquid  dissolves  the  salt,  both  opera- 
tions consuming  heat. 

253.  Heat  consumed  in  evaporation.  —  The  heat  consumed 
in  vaporization  is  greater  than  that  consumed  in  liquefaction  ; 
for  example,  in  the  case  of  water  it  is  greater  in  the  ratio  of 
536  :   80.     Hence    evaporation    is   the   more  efficient  means 
of  producing  extremely  low  temperatures.     Whatever  tends 
to  hasten  evaporation  tends   to  accelerate  the  reduction  of 
temperature.     Rapidity  of  evaporation  increases  with  the  tem- 
perature, extent  of  surf  ace  exposed,  diminution  of  pressure,  and 
dryness  of  the  atmosphere  (see  page  292).     The  more  volatile 
the  liquid  employed  for  evaporation,  other  things  being  equal, 
the  more  rapid  the  consumption  of  heat. 

Experiment  2.  —  Fill  the  palm  of  the  hand  with  ether ;  the  ether 
quickly  evaporates,  and  produces  a  sensation  of  cold. 

Experiment  3.  —  Place  water  at  about  40°  C.  in  a  thin  porous  cup, 
such  as  is  used  in  a  Grove's  battery,  and  the  same  amount  of  water  at 
the  same  temperature  in  a  glass  beaker  of  as  nearly  as  possible  the  same 
size  as  the  porous  cup.  Introduce  into  each  a  thermometer.  The  com- 
paratively large  amount  of  surface  exposed  by  means  of  the  porous  vessel 


290  MOLECULAR    DYNAMICS. 

will  so  hasten  the  evaporation  in  this  vessel,  that,  in  the  course  of  10  to  15 
minutes,  a  very  noticeable  difference  of  temperature  will  be  indicated  by 
the  thermometers  in  the  two  vessels. 

In  warm  climates  water  is  frequently  kept  in  porous 
earthen  vessels  in  order  that  its  temperature  may  be  kept  low 
enough  by  evaporation  to  render  it  suitable  for  drinking. 

Experiment  4.  —  Fill  an  atomizer,  such  as  is  used  in  the  toilet  for 
throwing  a  spray  of  cologne,  with  ether  and  throw  a  spray  of  the  liquid 
continuously  upon  the  bulb  of  a  thermometer.  In  a  very  short  time  the 
temperature  of  the  mercury  will  fall,  in  a  warm  room,  to  —  8°  C.  or  lower. 

Water  may  be  frozen  by  its  own  evaporation  in  the  receiver  of  an 
air-pump  from  which  the  air  (and  consequently  the  air-pressure)  is 
removed.  A  dish  of  sulphuric  acid  should  be  placed  in  the  receiver 
to  absorb  the  water-vapor. 

By  evaporating  liquid  ethylene  and  liquid  air  under  a  pressure  of 
4mm,  Olzewski  produced  a  temperature  of —  220°  C.1  The  cold 
produced  by  the  evaporation  of  liquid  carbon  dioxide  in  the  air, 
when  it  is  relieved  from  pressure,  is  sufficient  to  freeze  the  greater 
part  of  it,  producing  a  solid  mass  like  snow,  which  evaporates 
slowly,  producing  a  temperature  of  —  90°  C. 

254.    Spheroidal  state. 

A  drop  of  water  placed  on  a  smooth  metal  surface  heated  above 
200°  C.  will  not  come  in  contact  with  or  moisten  the  surface,  but 
assumes  the  form  of  a  flat  spheroid  and  rolls  about  like  a  ball  or 
spins  on  its  axis.  It  is  said  to  be  in  the  spheroidal  state.  When  in 
this  state  the  liquid  does  not  boil ;  indeed,  its  temperature  is  several 
degrees  below  its  boiling  point.  The  liquid  globule  rests  upon  a 
cushion  of  its  own  vapor  and  is  buoyed  up  by  it.  When,  however, 
the  heated  metal  cools  and  the  vapor  pressure  is  not  great  enough 
to  sustain  the  globule,  it  comes  in  contact  with  the  metal,  its  tem- 
perature rapidly  rises  to  the  boiling  point,  and  it  is  quickly  con- 
verted into  steam.  Showmen  place  red  hot  irons  in  their  mouths 
and  dip  their  moistened  hands  into  melted  lead  or  even  melted  iron, 

1  See  Philosophical  Magazine  (Feb.  1895).  The  announcement  is  just  made  in 
Nature  that  Olzewski  has  lately  succeeded  in  liquefying  hydrogen  and  producing  a 
temperature  of  —  243°  C. 


DEW-POINT.  291 

without  injury.     A  layer  of  spheroidal  fluid  prevents  contact  of  the 
flesh  with  the  heated  metal. 

Boutigny  placed  liquid  sulphur  dioxide,  whose  temperature  when 
in  the  spheroidal  state  is  below  zero,  in  a  red-hot  platinum  crucible  ; 
it  quickly  assumed  the  spheroidal  state,  and  drops  of  water  let  fall 
upon  it  quickly  froze.  Mercury  can  in  like  manner  be  frozen  in  a 
red-hot  crucible  by  employing  liquid  nitrous  oxide  in  the  spheroidal 
state. 


SECTION  XI. 

HYGROMETRY. 

255.  Dew-point.  —  Hygrometry  treats  of  the  state  of  the  air 
with  regard  to  the  water  vapor  it  contains.  A  given  space, 
e.g.  a  cubic  meter  (it  matters  little  whether  there  is  air  in  the 
space  or  whether  it  is  a  vacuum),  —  can  hold  only  a  limited 
quantity  of  water  vapor.  This  quantity  depends  on  the  tem- 
perature. The  capacity  of  a  space  for  water  vapor  increases 
rapidly  with  the  temperature,  being  nearly  doubled  by  a  rise 
of  10°  C.  On  the  other  hand  if  air  containing  a  given  quan- 
tity of  water  vapor  be  cooled,  it  will  continually  approach  and 
finally  reach  saturation,  since  the  lower  the  temperature,  the 
less  the  capacity  for  water  vapor.  It  is  evident  that  air 
saturated  with  vapor  cannot  have  its  temperature  lowered 
without  some  of  the  vapor  being  condensed  into  a  liquid, 
which  will  appear,  according  to  location  and  condition  of 
objects  within  it,  as  dew,  fog,  or  cloud.1  The  temperature  at 
which  this  condensation  occurs  is  called  the  dew-point  for  air 
containing  this  proportion  of  water  vapor.  The  dew  point 
may  be  defined  as  the  temperature  of  saturation  for  the 
quantity  of  water  vapor  actually  present  in  the  air.  The 

1  Clouds  formed  at  temperatures  above  0°  consist  of  minute  spherical  drops  of 
water,  ^^  to  TnlgiT  of  an  inch  or  more  in  diameter.  Clouds  formed  at  temperatures 
below  0°  consist  of  minute  ice  spicules,  which  may  increase  in  size  and  become 
snow-flakes. 


292 


MOLECULAR    DYNAMICS. 


greater  the  quantity  of  water  vapor  present  in  the  air. 
the  higher  is  its  dew-point.  Capacity  for  water  vapor  depends 
upon  temperature ;  dew-point  depends  upon  quantity  of  vapor 
present. 

If  the  existing  temperature  be  far  above  dew-point  it  in- 
dicates that  the  air  can  contain  much  more  vapor  than  there 
is  in  it  at  the  time,  and  the  air  is  said  to  be  dry.  If  the  tem- 
perature of  the  air  be  little  above 
dew-point,  the  air  is  said  to  be 
humid,  which  means  that  it 
can  hold  but  little  more  vapor. 
The  sensation  of  dryness  experi- 
enced, especially  in  rooms  heated 
artificially,  does  not  depend 
upon  the  absolute  quantity  of 
water  vapor  present  per  cubic 
foot. 

The  heat  of  a  stove,  for  in- 
stance, dries  the  air  of  a  room 
without  destroying  any  of  its 
water  vapor.  In  such  a  room, 
the  lips,  tongue,  throat,  and  skin 
experience  a  disagreeable  sensa- 
tion of  dryness,  owing  to  the 
rapid  evaporation  which  takes 
place  from  their  surfaces.  This 
should  be  taken  as  nature's  ad- 
monition to  keep  water  in  the  stove  urns,  and  in  tanks  con- 
nected with  furnaces. 

The  quantity  of  water  vapor  present  in  the  air  is  expressed 
either  (1)  by  the  mass  of  vapor  per  unit  of  volume  ;  or  (2)  by 
the  ratio  between  the  quantity  actually  present  and  that  which 
would  be  present  if  the  air  were  saturated  at  the  temperature 
of  observation.  The  latter  is  the  more  common  and  more 


FIG.  214. 


WET    AND    DRV    BULB    THERMOMETER. 


293 


useful  method,  and  this  ratio  is  called  the  relative  humidity, 
or  simply  "  humidity  "  of  the  air.  It  is  expressed  in  per- 
centages. Thus,  relative  humidity  =  75  per  cent.,  or  0.75, 
denotes  that  the  air  contains  three-fourths  the  quantity  of 
water  vapor  required  to  saturate  it  at  the  present  tempera- 
ture.1 

256.    Wet  and  dry  bulb  thermometer. 

The  relative  humidity  of  air  is  measured  in  various  ways  and  by 
various  devices.  The  instrument  most  commonly  used  is  Mason's 
wet  and  dry  bulb  thermometer,  or  as  it  is  frequently  called,  psy- 
cfirometer.  It  consists  (Fig.  214)  of  two  thermometers  mounted  side 
by  side  a  short  distance  apart,  one  having  a  dry  bulb  and  the  other 
a  bulb  covered  with  muslin,  kept  moist  by  capillary  action  through 

1  The  student  may  be  profited  by  a  perusal  of  the  following,  copied  from  the  daily 
meteorological  report  in  the  London  Times.  [Speed  the  time  when  our  own  govern- 
ment, in  consideration  of  its  educational  value  at  least,  shall  issue  daily  a  similarly 
complete  meteorological  bulletin.] 


THE  TIMES  OFFICE,  2  A.M. 

READINGS  OF  JORDAN  BAROMETER  (COR- 
RECTED) DURING  THE  HAST  TWEJfTY- 
FOTR  HOURS. 


TEMPERATURE  AND  HYOROMETRIC  CONDITION  OF  THE 
AIR  IN  LojrnoN.     AUGUST  25,  26. 


ACGIIST  25- 
§               A.M. 

-26 
] 

.  1 
^ 

*!ll 
1 

2 

^2 

fill 

Inches 

^.<Z 

321- 

J29-8 
-29-7 
J29-6 

320- 

-• 

319- 

318 

J 

r 

Hours 
of 
Obser- 
vation. 

Temperature. 

Tension 
of 
Vapour. 

Weight  of 

Vinpi°or 

cubic  feet 
of  air. 

l£S£* 

W.SK 
feet). 

Humidity 
(Satura- 
tion = 
100) 

Air. 

Dew 
Point. 

Noon.. 
9p.m.. 
2  a.m.. 

Degrees. 
62 
63 
62 

Degrees. 
52 
54 
55 

Inches. 
•388 
•418 
•433 

Grains. 
43 
46 
48 

Grains. 
19 

18 
14 

Per  Cent. 
69 
72 
77 

Minimum  Temperature,  55  deg.    Maximum  Tempera- 
ture, 63  deg. 

BEN  NEVIS  OBSERVATORY,  AUG.  25. 
STTMMIT  STATION,  (4,407  ft.  above  sea  level). 


•7 

Bar. 

Temperature. 

Wind. 

Cloud. 

At  32° 

Dry 
Bulb. 

Wet 
Bulb. 

Direc- 
tion. 

Force. 
Oto6. 

Species. 

Amount 
0  to  10. 

9A.M. 

In. 
24-820 

Deg. 
37-4 

Deg. 
Sat. 

S.W. 

1 

Mist 

10 

9P.M. 

24-605 

42-5 

Sat. 

S.W. 

0 

Mist 

10 

Maximum  temperature,  4;>  a;  minimum  temperature,  36'9. 
Black  bulb,  56.     Sunshine,  none.    Rainfall,  0-905  in. 
BASE  STATION  (42  ft.  above  sea  level). 


- 

Bar. 

Temperature. 

Wind. 

Cloud. 

At  32° 

Dry 
Bulb 

Wet 
Bulb 

Direc- 
tion. 

Force 
0  to  6 

Species. 

Amount 
0  to  10 

9A.M 
9P.M. 

In. 
29-189 
28-891 

Deg. 
53-8 
53-9 

Deg. 
52-8 
53-6 

S. 
Calm 

1 
0 

Cumulus 
Nimbus 

10 
10 

Maximum  temperature,  57-4;  minimum  temperature,  51-3. 
Black  bulb,  110.  Sunshine,  1  hour  19  min.  Rainfall, 
0-520  in. 


294  MOLECULAR    DYNAMICS. 

conducting  threads  of  lamp-wick  from  a  vessel  of  water  below.  The 
dry  bulb  indicates  the  temperature  of  the  air  itself ;  while  the  wet 
bulb,  cooled  by  evaporation,  shows  usually  a  lower  temperature 
according  to  the  amount  and  rapidity  of  evaporation.  The  differ- 
ence in  temperature  of  the  two  bulbs  is  greatest  when  the  air  is 
dryest. 

By  experiment  has  been  ascertained  the  relative  humidity 
corresponding  to  1,  2,  etc.  degrees  difference  between  the  two 
thermometers  for  any  given  temperature  of  the  air.  Empirical 
psychrometrical  tables  similar  to  the  reduced  table  in  the  Appendix 
(p.  000)  accompany  this  instrument.  The  observer  reads  the  tem- 
perature of  the  air  and  ascertains  the  difference  of  the  temperatures 
of  the  two  bulbs,  and  from  these  two  numbers  determines  by  the 
table  the  relative  humidity,  and  the  dew-point  of  the  air  at  that 
time  and  place. 

Not  only  does  hygrometry  play  an  important  part  in  the  science 
of  meteorology,  and  consequently  have  important  bearings  upon 
many  branches  of  industry,  but  it  also  has  an  intimate  relation  to 
the  hygienic  qualities  of  the  atmosphere.  The  human  body  is  much 
affected  by  the  hygrometric  state  of  the  air. 


SECTION  XII. 

DIFFUSION    OB    TRANSFERENCE    OF    HEAT. 

There  is  always  a  tendency  to  equalization  of  temperature  ; 
that  is,  heat  has  a  tendency  to  pass  from  a  warmer  body  to  a 
colder,  or  from  a  warmer  to  a  colder  part  of  the  same  body, 
until  there  is  an  equality  of  temperature. 

There  are  commonly  recognized  three  processes  of  diffusion 
of  heat,  —  conduction,  convection,  and  radiation. 

257.    Conduction. 

Experiment  1.  —  Place  one  end  of  a  wire  about  10  inches  long  in  a 
lamp-flame,  and  hold  the  other  end  in  the  hand.  Heat  gradually  travels 
from  the  end  in  the  flame  toward  the  hand.  Apply  your  fingers  succes- 
sively at  different  points  nearer  and  nearer  the  flame  ;  you  find  that  the 
nearer  you  approach  the  flame,  the  hotter  the  wire  is. 


CONDUCTION.  295 

The  flow  of  heat  through  an  unequally  heated  body,  from 
places  of  higher  to  places  of  lower  temperature,  is  called 
conduction;  the  body  through  which  it  travels  is  called  a 
conductor.  The  molecules  of  the  wire  in  the  flame  have  their 
motion  quickened;  they  strike  their  neighbors  and  quicken 
their  motion ;  the  latter  in  turn  quicken  the  motion  of 
the  next  ;  and  so  on,  until  some  of  the  motion  is  finally 
communicated  to  the  hand,  and  creates  in  it  the  sensation  of 
heat. 

Experiment  2.  —  Fig.  215  represents  a  board  on  which  are  fastened, 
by  means  of  staples,  four  wires :  (1)  iron,  (2)  copper,  (3)  brass,  and  (4) 
German  silver.  Place  a  lamp-flame  where  the  wires 
meet.  In  about  a  minute  run  your  fingers  along 
the  wires  from  the  remote  ends  toward  the  flame, 
and  see  how  near  you  can  approach  the  flame  on 
each  without  suffering  from  the  heat.  Make  a  list 
of  these  metals,  arranging  them  in  the  order  of  their 
conductivity. 

Experiment  3.  —  Go  into  a  cold  room,  and  place  FlG  215 

the  bulb  of  a  thermometer  in  contact  with  various 
substances  in  the  room  ;  you  will  probably  find  that  they  have  the  same, 
or  very  nearly  the  same,  temperature.  Place  your  hand  on  the  same 
substances ;  they  appear  to  have  very  different  temperatures.  This  is 
due  to  the  fact  that*some  substances  conduct  heat  away  from  the  hand 
faster  than  others.  Those  substances  that  appear  coldest  are  the  best 
conductors.  If  you  go  into  a  room  warmer  than  your  body,  all  this  is 
reversed ;  those  substances  which  feel  warmest  are  the  best  conductors, 
because  they  conduct  their  own  heat  to  your  hand  fastest. 

You  learn  that  some  substances  conduct  heat  much  more 
rapidly  than  others.  The  former  are  called  good  conductors, 
the  latter  poor  conductors.  Metals  are  the  best  conductors, 
though  they  differ  widely  among  themselves. 

Experiment  4.  —  Nearly  fill  a  test-tube  with  water,  and  hold  it  some- 
what inclined  (Fig.  216),  so  that  a  flame  may  heat  the  part  of  the  tube 
near  the  surface  of  the  water.  Do  not  allow  the  flame  to  touch  the  part 


296  MOLECULAR    DYNAMICS. 

of  the  tube  that  does  not  contain  water.  The  water  may  be  made  to 
boil  near  its  surface  for  several  minutes  before  any  change  of  the  tem- 
perature at  the  bottom  will  be  perceived. 

Liquids,  as  a  class,  are  poorer  con- 
ductors than  solids.  Gases  are  much 
poorer  conductors  than  liquids.  It  is 
difficult  to  discover  that  pure,  dry  air 
possesses  any  conducting  power.  The 
poor  conducting  power  of  our  clothing 
is  due  partly  to  the  poor  conducting 
power  of  the  fibers  of  the  cloth,  but 
chiefly  to  the  air  which  is  confined  by  it. 

Loose  garments,  and  garments  of  loosely  woven  cloth,  inas- 
much as  they  hold  a  large  amount  of  confined  air,  furnish  a 
good  protection  from  heat  and  cold.  Bodies  are  surrounded 
with  bad  conductors,  to  retain  heat  when  their  temperature  is 
above  that  of  surrounding  objects,  and  to  exclude  it  when 
their  temperature  is  below  that  of  surrounding  objects.  In 
the  same  manner  double  windows  and  doors  protect  from 
cold. 

258.  Convection  in  gases.  —  Conduction  takes  place  gradu- 
ally and  slowly  at  best  from  particle  to  particle,  the  body 
and  its  particles  being  relatively  at  rest.  Convection  takes 
place  when  the  body  moves  or  there  is  relative  motion  be- 
tween its  parts,  thus  carrying  heat. 

Experiment  5.  — Hold  your  hand  a  little  way  from  a  flame,  beneath, 
on  the  side  of,  and  above  the  flame.  At  which  place  is  the  heat  most 
intense  ? 

Experiment  6.  — Cover  a  candle-flame  with  a  glass  chimney  (Fig.  217), 
blocking  the  latter  up  a  little  way  so  that  there  may  be  a  circulation  of 
air  beneath.  Hold  smoking  touch-paper  near  the  bottom  of  the  chimney  ; 
the  smoke  seems  to  be  drawn  with  great  rapidity  into  the  chimney  at  the 
bottom  ;  in  other  words,  the  office  of  the  chimney  is  to  create  what  is 
called  a  draft  of  air.  Notice  whether  the  combustion  takes  place  any 
more  rapidly  with  than  without  the  chimney. 


CONVECTION    IN    GASES. 


297 


Experiment  7.  —  Place  a  candle  within  a  circle  of  holes  cut  in  the  cover 
of  a  vessel,  and  cover  it  with  a  chimney,  A  (Fig.  218).  Over  an  orifice 
in  the  cover  place  another  chimney,  B.  Hold  a  roll  of  smoking  touch- 
paper  over  B.  The  smoke  descends  this  chimney,  and  passes  through 
the  vessel  and  out  at  A.  This  illustrates  the  method  often  adopted  to 
produce  a  ventilating  draft  through  mines.  Let  the  interior  of  the  tin 
vessel  represent  a  mine  deep  in  the  earth,  and  the  chimneys  two  shafts 
sunk  to  opposite  extremities  of  the  mine.  A  fire  kept  burning  at  the 
bottom  of  one  shaft  will  cause  a  current  of  air  to  sweep  down  the  other 
shaft,  and  through  the  mine,  and  thus  keep  up  a  circulation  of  pure  air 
through  the  mine. 


FIG.  217. 


Fro.  218. 


The  cause  of  the  ascending  currents  is  evident.  Air,  on  becoming 
heated,  expands  rapidly  and  becomes  much  rarer  than  the  surrounding 
colder  air  ;  hence  it  rises  much  like  a  cork  in  water,  while  cold  air  pours 
in  laterally  to  take  its  place.  In  this  manner  winds  are  created.  Sea 
and  land  breezes  are  convection  currents. 


The  so-called  trade-winds  originate  in  the  torrid  or  heated 
zone  of  the  earth.  The  air  over  the  heated  surface  of  the 
earth  rises,  and  the  colder  air  from  the  polar  regions  flows  in 


298  MOLECULAR   DYNAMICS. 

on  both  sides,  giving  rise  to  a  constant  wind  from  the  N.E.1 
in  the  northern  hemisphere,  and  a  wind  from  the  S.E.  in  the 
southern  hemisphere.  Convection  currents  on  the  surface  of 
the  sun  often  attain  a  velocity  of  100  miles  per  second. 

259.  Change  of  temperature  in  vertical  currents  ascending 
from  the  earth. 

The  lower  air  in  contact  with  the  heated  surface  of  the  earth 
acquires  a  certain  temperature  and  a  corresponding  expansive  force 
previous  to  its  ascent.  As  it  reaches  higher  altitudes,  the  pressure 
upon  it  becomes  less ;  it  therefore  expands,  pushing  away  the  sur- 
rounding air,  until,  as  a  result  of  its  expansion,  its  expansive  force 
is  reduced  to  equality  with  the  pressure  upon  it.  It  follows  from 
the  dynamical  theory  of  heat,  that  in  doing  this  work  the  ascending 
air  must  expend  some  of  its  energy  :  i.e.  the  work  is  done  by  the 
expenditure  of  some  of  its  heat ;  hence,  the  ascending  air  is  cooled 
by  the  very  processes  involved  in  its  ascent.  The  rate  of  cooling 
thus  produced  is  about  1°  for  100  m  of  ascent.  Such  changes  are 
called  adiabatic;  i.e.  they  are  produced  without  a  transfer  of 
heat. 

260.  Ventilation.  —  Intimately  connected  with   the    topic 
convection,   is  the    subject  (of   vital   importance)  ventilation, 
inasmuch  as  our  chief  means  of  securing  the  latter  is  through 
the  agency  of  the  former.      The  chief  constituents  of  our 
atmosphere  are  nitrogen  and  oxygen,  with  varying  quantities 
of  water  vapor,  argon,  carbon  dioxide  gas,  ammonia  gas,  nitric 
acid  vapor,  and  other  gases.     The  atmosphere  also  contains  in 
a  state  of  suspension  varying  quantities  of  small  particles  of 
free  carbon  in  the  form  of  smoke,  microscopic  organisms,  and 
dust  of  innumerable  substances.     All  of  these  constituents 
except  the  first  four  are  called  impurities.     Carbon  dioxide 
is  the  impurity  that  is  usually  the  most  abundant  and  most 
easily  detected  ;  so  it  has  come  to  be  taken  as  the  measure 
of  the  purity  of  the  atmosphere,  though  not  itself  the  most 

1  The  easterly  component  is  due  to  the  earth's  rotation. 


VENTILATION. 


299 


deleterious  constituent.  Its  chief  harm  arises  from  its  diluent 
effect  upon  the  life-giving  oxygen.  Pure  out-door  air  contains 
about  4  parts  of  carbon  dioxide  by  volume  in  10,000.  If  the 
quantity  rise  to  10  parts,  the  air  becomes  unwholesome. 

Experiment  8. — Ascertain  by  means  of  Wolpert's  air-tester1  (ap- 
proximately) the  number  of  parts  in  10,000  of  carbonic  acid  gas  (and 
thereby  determine  approximately  the  degree  of  pollution  by 
respiration  and  combustion)  in  the  air  of  the  school-room. 

Clean  the  test-tube  with  water  containing  a  little  vinegar, 
and  afterwards  rinse  thoroughly  with  clean  water.  Fill  the 
clean  test-tube  with  lime-water,  even  with  the  horizontal 
mark.  Expel  all  the  air  possible  from  the  rubber  bulb  A 
(Fig.  219),  by  pressing  on  it  with  the  thumb  ;  then  allow  it 
to  fill  with  air  from  the  room.  Insert  the  small  glass  tube 
B  into  the  lime-water  nearly  to  the  bottom.  Expel  the 
air  in  the  bulb  again  with  moderate  rapidity,  so  that  the 
bubbles  may  rise  nearly  to  the  top  of  the  tube  C ;  but  do 
not  allow  the  liquid  to  overflow.  Continue  the  pressure 
until  you  have  withdrawn  the  tube  from  the  liquid,  when 
you  will  allow  the  bulb  to  refill  with  air  of  the  room.  At 
the  end  of  each  expulsion  place  the  bottom  of  the  test- 
tube  on  a  sheet  of  white  paper  in  good  daylight,  and  look 
vertically  down  through  the  liquid  at  the  black  mark  on  the 
bottom  of  the  test-tube ;  repeat  the  process,  ,being  careful 
not  to  affect  the  result  more  than  is  necessary  with  your 
breath,  until  the  turbidity  of  the  lime-water  renders  the 
mark  invisible.  "  If  the  mark  become  obscured  after  filling  pIG  219 
the  bulb  ten  or  fifteen  times  only,  the  air  of  the  apartment 
is  unfit  for  continuous  respiration.  With  good  air  the  bulb  must  be  filled 
twenty-five  times  and  upwards.  The  normal  amount  in  pure  out-door 
air  is  3  to  5  parts  per  10,000." 

Ascertain,  by  comparing  your  results  with  those  given  by  Prof.  Wol- 
pert  in  the  table  below,  the  number  of  parts  of  carbon  dioxide  in  10,000 
of  the  air  of  your  room.  Repeat  the  experiment,  taking  air  at  different 
elevations  in  the  room. 


1  This  instrument  is  used  almost  exclusively  by  inspectors  of  school  and  other 
public  buildings  in  the  State  of  Massachusetts, 


300 


MOLECULAR    DYNAMICS. 


Number 

Carbon 

Number 

Carbon 

Number 

Carbon 

Number 

Carbon 

of 

dioxide 

of 

dioxide 

of 

dioxide 

of 

dioxide 

Fillings. 

per  10,000. 

Fillings. 

per  10,000. 

Fillings. 

per  10,000. 

Fillings. 

per  10,000. 

1 

200. 

16 

12.5 

31 

6.4 

i 
46 

4.3 

'2 

100. 

17 

12. 

32 

6.3 

47 

4.2 

3 

67. 

18 

11. 

33 

6.1 

48 

4.1 

4 

50. 

19 

10.5 

34 

5.9 

49 

4.1 

5 

40. 

20 

10. 

35 

5.7 

50 

4.0 

6 

33. 

21 

9.5 

36 

5.5 

51 

3.9 

7 

29. 

22 

9.1 

37 

5.4 

52 

3.9 

8 

25. 

23 

8.7 

38 

5.3 

53 

3.8 

9 

22. 

24 

8.3 

39 

5.1 

54 

3.7 

10 

20. 

25 

8. 

40 

5. 

55 

3.7 

11 

18. 

26 

7.7 

41 

4.9 

56 

3.6 

12 

16. 

27 

7.4 

42 

4.8 

57 

3.5 

13 

15. 

28 

7.1 

43 

4.6 

58 

3.5 

14             14. 

29 

6.9 

44 

4.5 

59 

3.4 

15             13. 

30 

6.6 

45 

4.4 

60            3.3 

Carbon  dioxide  is  about  one  and  one-half  times  heavier  than 
air  at  the  same  temperature ;  consequently,  when  both  have 
the  same  temperature,  and  the  former  is  very  abundant,  it 
tends  to  sink  beneath  the  air,  in  which  large  quantities  of 
this  gas  are  generated. 

The  knowledge  of  this  fact  has  led  many  to  suppose  that  a 
means  for  the  escape  of  impure  air  need  be  provided  only 
near  the  floor  of  a  room.  But  it  should  be  remembered  that 
(1)  the  tendency  of  carbon  dioxide,  unless  present  in  excessive 
quantities,  is  to  diffuse  itself  equally  through  a  body  of  air ; 
but  (2)  when  it  is  heated  to  a  temperature  above  that  of  the 
surrounding  air,  as  when  generated  by  flames,  or  when  it 
escapes  in  the  warm  breath  of  animals,  it  is  lighter  than  the 
air,  and  consequently  rises.  If  this  impure  air  could  escape 
at  the  ceiling  while  fresh  air  entered  at  the  floor,  the  ventila- 
tion would  be  good.  But  usually  this  fresh  air  must  be 
warmed ;  and  in  passing  over  a  stove,  furnace,  or  steam 
radiator,  its  temperature  will  generally  become  higher  than 


VENTILATION. 


301 


that  of  the  impure  air,  so  that  it  will  rise  above  the  latter, 
and  pass  out  at  a  ventilator  in  the  ceiling,  leaving  the  floor 
cold  ;  hence,  in  high  school-rooms  the  most  impure  air  is 
often  found  half-way  up. 

The  quantity  of  fresh  air  introduced  must  be  great  enough 
to  dilute  the  impurities  till  they  are  harmless.  An  adult 
makes  about  18  respirations  per  minute,  expelling  from  his 
lungs  at  each  expiration  about  500  cc  of  air,  over  4  per  cent 
of  which  is  carbon  dioxide.  At  this  rate,  about  9,000  cc  of  air 
per  minute  become  unfit  for  respiration ;  and  to  dilute  this 
sufficiently,  good  authorities  say  that  about  100  times  as  much 
fresh  air  is  needed ;  or,  for 
proper  ventilation,  about  a 
cubic  meter  of  fresh  air  per 
minute  is  needed  for  each  per- 
son, or,  in  British  measures, 
2,000  cubic  feet  per  hour. 

Fig.  220  represents  a  scheme 
for  heating  a  room  by  steam, 
and  ventilating  it  by  con- 
vection. Steam  is  conveyed 
by  a  pipe  from  the  boiler 
to  a  radiator  box  just  be- 
neath the  floor  of  the  room. 
The  air  in  the  box  becomes 
heated  by  contact  with  and 
radiation  from  the  coil  of 
pipe  in  the  box,  and  rises 
through  a  passage  opening 
into  the  room  by  means  of  a 
register  near  the  floor  at  C,  a 
supply  of  pure  air  being  kept 
up  by  means  of  a  tubular  Fro 

passage  opening  into  the  box 
from  the  outside  of  the  building.  Thus  the  room  is  furnished  with 
pure  warm  air,  which,  mingling  with  the  impurities  arising  from  the 
respiration  of  its  occupants,  serves  to  dilute  them  and  render  them 


302  MOLECULAR    DYNAMICS. 

less  injurious.  At  the  same  time,  the  warm  and  partially  vitiated 
air  of  the  room  passes  through  the  open  ventilator  A  into  the 
ventilating-flue,  and  escapes,  so  that  in  a  moderate  length  of  time 
a  nearly  complete  change  of  air  is  effected.  It  is  evident  that  on 
the  coldest  days  of  winter  the  convection  is  most  rapid  ;  indeed,  it 
may  be  so  rapid  that  the  air  cannot  be  heated  sufficiently  to  render 
the  room  near  the  floor  comfortable.  At  such  times  the  ventilator 
A  may  be  closed,  while  the  ventilator  B  is  always  open.  The 
heated  air  rises  to  the  top  of  the  room  and,  not  being  able  to  escape, 
crowds  the  colder  air  beneath  out  at  the  ventilator  B.  No  system 
of  ventilation  dependent  wholly  on  convection  is  adequate  properly 
to  ventilate  crowded  halls ;  air  is  too  viscous  and  sluggish  in  its 
movements.  In  such  cases  ventilation  should  be  assisted  by  some 
mechanical  means,  such  as  a  blower  or  fan,  worked  by  steam  or 
water  power. 

261.    Convection  in  liquids. 

Experiment  9.  —  Fill  a  small  (6  ounce)  thin  glass  flask  with  boiling  hot 
water,  color  it  with  a  teaspoonful  of  ink,  stopper  the  flask,  and  lower  it 
deep  into  a  tub,  pail,  or  other  large  vessel  filled  with  cold  water.  With- 
draw the  stopper,  and  the  hot,  rarer,  colored  water  will  rise  from  the 
flask,  and  the  cold  water  will  descend  into  the  flask.  The  two  currents 
passing  into  and  out  of  the  neck  of  the  flask  are  easily  distinguished. 
The  colored  liquid  marks  distinctly  the  path  of  the  heated  convection 
currents  through  the  clear  liquid  and  makes  clear  the  method  by  which 
heat,  when  applied  at  the  bottom  of  a  body  of  liquid,  becomes  rapidly 
diffused  through  the  entire  mass  notwithstanding  that  liquids  are  poor 
conductors. 

Experiment  10.  —  Fill  again  the  flask  with  hot  colored  water,  stopper, 
invert,  and  introduce  the  mouth  of  the  flask  just  beneath  the  surface  of  a 
fresh  pail  of  cold  water.  Withdraw  the  stopper  with  as  little  agitation 
of  the  water  as  possible.  What  happens  ?  Explain. 

Ocean  currents,  e.g.  the  gulf  stream,  are  convection  currents. 
Liquids  are  also  cooled  by  convection  currents.  When  the 
air  above  the  surface  of  a  pond,  for  instance,  is  cooler  than 
the  surface  water,  the  latter  gives  heat  to  the  former,  cools, 
becomes  denser,  and  sinks.  Meanwhile  the  warmer  and  rarer 
water  below  rises,  and  in  this  way  the  entire  body  is  kept  at 


RADIATION.  303 

an  approximately  uniform  temperature  until  it  reaches  4°  C., 
at  which  point  convection  ceases. 

262.  Radiation.  —  In  radiation  a  hotter  body  loses  heat, 
and  a  colder  body  is  warmed,  through  the  transmission  of 
undulatory  motion  in  a  medium  called  the  ether,  which  is  not 
itself  heated  thereby.  It  is  neither  a  mass  nor  a  molecular 
transference  of  heat;  in  fact  heat  itself  is  not  transferred 
by  radiation  at  all.  Heat  generates  radiation  (ether  wave 
motions)  at  one  place,  and  the  body  which  obstructs  these 
waves  transforms  the  energy  of  their  motion,  or  as  it  is  com- 
monly called  radiant  energy,  into  heat.  In  this  manner  the 
earth  is  heated  by  the  sun,  though  no  heat  passes  between 
them.  In  this  manner  radiant  energy  passes  through  glass 
and  slabs  of  ice  without  heating  them  much,  since  they  offer 
little  obstruction  to  the  passage  of  ether  waves.  All  bodies 
emit  radiant  energy,  and  there  is  an  exchange  of  energy 
between  bodies  by  radiation,  going  on  at  all  times.  This 
mode  of  transmission  of  energy  is  the  most  important  of  all, 
and  will  be  treated  fully  in  the  next  chapter. 


SECTION  XIII. 

THERMO-DYNAMICS. 

263.  Thermo-dynamics   defined.  —  Thermo-dynamics   treats 
of  the  relation  between  heat  and  mechanical  work.     One  of  the 
most  important  discoveries  in  science  is  that  of  the  equivalence, 
of  heat  and  work  /  that  is,  that  a  definite  quantity  of  mechanical 
work,  when  transformed  without  waste,  yields  a  definite  quantity 
of  heat ;  and  conversely,  this  heat,  if  there  be  no  waste,  can  per- 
form the  original  quantity  of  mechanical  work. 

264.  Transformation,  correlation,  and  conservation,  of  energy. 
—  The  proof  of  the  facts  just  stated  was  one  of  the  most 
important  steps  in  the  establishment  of  the  grand  twin  con- 


304  MOLECULAR    DYNAMICS. 

ceptions  of  modern  science  :  (1)  that  all  kinds  of  energy  are 
so  related  to  one  another  that  energy  of  any  kind  can  be  trans- 
formed into  energy  of  any  other  kind,  —  known  as  the  doctrine 
of  CORRELATION  OF  ENERGY  ;  (2)  that  when  one  form  of 
energy  disappears,  its  exact  equivalent  in  another  form  always 
takes  its  place,  so  that  the  sum  total  of  energy  is  unchanged,  — 
known  as  the  doctrine  of  CONSERVATION  OF  ENERGY. 

These  two  doctrines  are  admirably  summarized  by  Maxwell 
as  follows  :  "The  total  energy  of  any  body  or  system  of  bodies  is 
a  quantity  which  can  neither  be  increased  nor  diminished  by 
any  mutual  action  of  these  bodies,  though  it  may  be  transformed 
into  any  of  the  forms  of  which  energy  is  susceptible."  Since  all 
bodies  of  matter  in  the  universe  constitute  a  system,  it 
follows  from  the  above  that  the  sum  total  of  energy  in  the 
universe  is  a  constant  quantity.  Neither  creation  nor  annihi- 
lation of  energy  is  possible  through  any  agenc}^  known  to 
man.  These  doctrines  constitute  the  corner  stones  of  modern 
physical  science.  Chemistry  teaches  that  there  is  a  conser- 
vation of  matter,  i.e.  that  matter  is  neither  creatable  nor 
annihilable  through  any  known  natural  agency  or  process. 

265.    Joule's  experiment.  —  Two  laius  of  t  her  mo-dynamics.  — 
The  experiment  to  ascertain  the  "  mechanical  value  of  heat," 
as  performed  by  Dr.  Joule  of  England,  was  conducted  about 
as  follows : 

A  copper  vessel,  B  (Fig.  221),  was  provided  with  a  paddle 
wheel  (indicated  by  the  dotted  lines),  which  rotated  about  a 
vertical  axle,  A.  The  axle  was  rotated  by  the  weights  E  and 
F,  the  cord  of  each  being  so  arranged  that  each  weight,  in 
falling,  rotated  the  axle  in  the  same  direction.  By  turning 
the  crank  above  A  the  weights  are  raised  to  any  desired  hight 
measured  on  the  scales  G  and  H. 

The  resistance  offered  by  the  water  to  the  motion  of  the 
paddles  was  the  means  by  which  the  mechanical  energy  of 
the  weights  was  converted  into  heat,  which  raised  the  tern- 


JOULE'S    EXPERIMENT. 


305 


perature  of  the  water.  Taking  two  bodies  whose  combined 
mass  was,  e.g.,  80  K,  he  raised  them  a  measured  distance,  e.g. 
53m  high;  by  so  doing  4240 kgm  of  work  were  performed  upon 
them,  and  consequently  an  equivalent  amount  of  energy  was 
stored  up  in  them,  ready  to  be  converted,  first  into  that  of 
mechanical  motion,  then  into  heat.  He  took  a  definite  mass 
of  water  to  be  agitated,  e.g.  2  K,  at  a  temperature  of  0°  C. 
After  the  descent  of  the  weights,  the  water  was  found  to  have 
a  temperature  of  5°  C.  ;  consequently  the  2  K  of  water  must 
have  received  10  calories  of  heat  (careful  allowance  being 


made  for  all  losses  of  heat),  which  is  the  number  of  calories 
that  is  equivalent  to  4240  kgm  of  mechanical  energy  ;  or  one 
calorie  is  equivalent  to  424  kgm  (commonly  taken  as  4.2  X  107 
ergs)  of  mechanical  energy. 

In  other  words,  to  produce  the  quantity  of  heat  required  to 
raise  1  kilogram  of  water  through  1°  C.,  4%4  kilogrammeters  of 
mechanical  energy  must  be  consumed.  What  the  experiment 
really  shows  is  that  whenever  a  certain  quantity  of  mechanical 
energy  is  converted  into  heat,  the  number  of  thermal  units 
produced  is  always  proportional  to  the  mechanical  energy 
consumed,  or. to  the  work  done.  This  is  embodied  in  the 


306  MOLECULAR    DYNAMICS. 

first  law  of  thermodynamics,  which  is  expressed  as  follows  : 
"  When  equal  quantities  of  mechanical  effect  are  produced  by 
any  means  whatever  from  purely  thermal  sources,  or  lost  in 
purely  thermal  effects,  equal  quantities  of  heat  are  put  out  of 
existence,  or  are  generated"  It  is  apparent  that  heat,  being  a 
form  of  energy,  may  be  measured  in  ergs.  In  this  way  the 
erg  is  regarded  as  the  mechanical  unit  of  heat.  The  advan- 
tage of  this  is  found  in  the  fact  that  we  are  often  in  the 
position  of  having  to  solve  problems  in  which  heat  and  work 
enter  as  terms  to  be  added  together.  The  existence  of 
quantitative  correlations  between  all  the  various  forms  of 
energy  imposes  upon  men  of  science  the  duty  of  bringing  all 
kinds  of  physical  quantities  to  one  common  scale  of  com- 
parison, as  is  attempted  in  the  absolute  system. 

Mechanical  energy  can  be  wholly  converted  into  heat,  but 
it  can  be  demonstrated  that  heat  under  the  most  favorable 
circumstances  conceivable,  even  with  the  use  of  an  ideally 
perfect  heat  engine  (i.e.  one  which  wastes  no  heat),  can  never 
be  wholly  converted  into  work.  A  portion  —  a  large  portion 
—  of  the  heat  employed  must  be  given  up  to  some  substance 
termed  technically  a  "  refrigerator,''  which  in  some  form  is  a 
necessary  adjunct  to  every  heat-engine,  and  that  portion  still 
exists  as  heat.  This  is  a  practical  deduction  from  the  so- 
called  Second  Law  of  Thermodynamics ; 1  viz.,  "  It  is  impos- 
sible to  derive  mechanical  effect  from  any  portion  of  matter  by 
cooling  it  below  the  temperature  of  the  coolest  surrounding  ob- 
jects." The  ratio  of  the  heat  converted  into  work  and  the 
entire  heat  employed  is  called  the  efficiency  of  the  engine. 
"  For  any  boiler-pressure  "  (of  a  steam-engine)  "  which  it  is 
safe  to  employ  in  practice,  it  is  not  possible,  even  with  a 
perfect  engine,  to  convert  into  work  more  than  about  fifteen 
per  cent,  of  the  heat  used."  —  ANTHONY  AND  BKACKETT. 

1  Any  adequate  discussion  of  this  law  would  take  us  beyond  the  limits  proposed 
for  this  book.  This  subject  is  more  fully  treated  in  the  works  of  Barker  and  Daniell. 


MECHANICAL   EQUIVALENT    OF    HEAT. 


307 


266.  Mechanical  equivalent  of  heat.  —  As  a  converse  of  the 
above  it  may  be  demonstrated  by  actual  experiment  that  the 
quantity  of  heat  required  to  raise  1  K  of  water  from  0°  to 
1°  C.  will,  if  converted  into  work,  raise  a  424  K  weight  1  m 
high,  or  1  K  weight  424  m  high.  According  to  the  British 
system,  the  same  fact  is  stated  as  follows  :  The  quantity  of 
heat  that  will  raise  the  temperature  of  1  pound  of  water  from 
60°  to  61°  F.  will  raise  772.55  pounds  1  foot  high.  The 
quantity,  424  kgm,  is  called  the  mechanical  equivalent  of  one 
calorie,  or  Joule? s  equivalent  (abbreviated  simply  J).  J  is 
the  number  of  units  of  energy  or  work  per  unit  of  heat.  Or  we 
may  say  that  one  calorie  is  the  thermal  equivalent  of  424  kgm 
of  work,1  or  the  thermal  equivalent  of  1  kgm  is  ±^  calorie. 


Temperature, 
Centigrade. 

Equivalent  in 
Kilogrammeters. 

Temperature, 
Centigrade. 

Equivalent  in 
Kilogrammeters. 

0° 

431.1 

23° 

426.0 

5° 

429.8 

•25° 

425.8 

10° 

428.5 

27° 

425.6 

15° 

427.4 

29° 

425.5 

17° 

427.0 

31° 

425.6 

19° 

426.6 

33° 

425.7 

21° 

426.2 

35° 

425.8 

If  we  denote  by  If  the  number  of  calories,  and  by  TFthe 
number  of  kilogrammeters  of  mechanical  energy,  then  the 


ratio  —  :  =  -  (a  constant)  =  ¥ 


whence  H  =  —  . 


1  A  knowledge  of  the  exact  numerical  value  is  of  great  scientific  and  practical 
importance.  The  results  as  obtained  by  Rowland  (1879)  with  improved  apparatus 
and  by  improved  methods,  though  the  same  in  principle  as  that  employed  by  Joule, 
are  doubtless  more  accurate  and  are  likely  to  come  into  general  use  for  engineering 
and  scientific  purposes. 

«  The  following  table  gives  the  number  of  kilogrammeters  required  to  raise  one 
kilogram  of  pure  water  from  t"  to  t°  +  1,  as  found  by  Rowland,  for  the  latitude  of 
Baltimore,  and  at  sea-level.  At  Baltimore,  g  =  980.05  cm.  To  reduce  to  any  other 
latitude  than  Baltimore,  add,  for  lat.  30°,  0.34  kgm  ;  lat.  40°,  0.08  kgm  ;  lat.  50°, 
—  0.41  kgm.  The  value  of  J  ordinarily  used  in  engineering  computations  is  424  kgm. 
As  most  measurements  with  which  this  value  of  J  is  employed  are  made  at  about  15" 
to  25°  C.,  this  value  is  too  small  by  one-half  per  cent,  or  more." 


308  MOLECULAR    DYNAMICS. 


SECTION  XIV. 

THERMODYNAMICS    CONTINUED. STEAM-ENGINE. 

267.  Description  of  a  steam-engine.  —  A  steam-engine  is  .a 
machine  in  which  the  elastic  force  of  steam  is  the  motive 
agent.  Inasmuch  as  the  elastic  force  of  steam  is  entirely  due 
to  heat,  the  steam-engine  is  properly  a  heat  engine  ;  that  is,  it 
is  a  machine  by  means  of  which  heat  is  continuously  trans- 
formed into  work,  or  the  energy  of  mass  motion. 

The  modern  steam-engine  consists  essentially  of  an  arrange- 
ment by  which  steam  from  a  boiler  is  conducted  to  each  side 
of  a  piston  alternately ;  and  then,  having  done  its  work  in 
driving  the  piston  to  and  fro,  is  discharged  from  each  side 
alternately,  either  into  the  air  or  into  a  condenser.  The 
diagram  in  Fig.  222  will  serve  to  illustrate  the  general  fea- 
tures and  the  operation  of.  a  steam-engine.  The  details  of  the 
various  mechanical  contrivances  are  purposely  omitted,  so  as 
to  present  the  engine  as  nearly  as  possible  in  its  simplicity. 

In  the  diagram,  B  represents  the  boiler,  F  the  furnace,  S 
the  steam-pipe  through  which  steam  passes  from  the  boiler  to 
a  small  chamber  VC,  called  the  valve-chest.  In  this  chamber 
is  a  slide-valve  V,  which,  as  it  is  moved  to  and  fro,  opens  and 
closes  alternately  the  passages  M  and  N  leading  from  the 
valve-chest  to  the  cylinder  C,  and  thus  admits  the  steam 
alternately  each  side  of  the  piston  P.  When  one  of  these 
passages  is  open,  the  other  is  always  closed.  Though  the 
passage  between  the  valve-chest  and  the  space  in  the  cylinder 
on  one  side  of  the  piston  is  closed,  thereby  preventing  the 
entrance  of  steam  into  this  space,  the  passage  leading  from 
the  same  s.pace  is  open  through  the  interior  of  the  valve,  so 
that  steam  can  escape  from  this  space  through  the  exhaust- 
pipe  E.  Thus,  in  the  position  of  the  valve  represented  in  the 
diagram,  the  passage  N  is  open,  and  steam  entering  the  cylin- 


DESCRIPTION    OF    A    STEAM-ENGINE. 


309 


der  at  the  top  drives  the  piston  in  the  direction  indicated  by 
the  arrow.  At  the  same  time  the  steam  on  the  other  side  of 
the  piston  escapes  through  the  passage  M  and  the  exhaust- 
pipe  E.  While  the  piston  moves  to  the  left,  the  valve  moves 
to  the  right,  arid  eventually  closes  the  passage  N  leading 
from  the  valve-chest  and  opens  the  passage  M  into  the  same, 
and  thus  the  order  of  things  is  reversed. 


FIG.  222. 

Motion  is  communicated  by  the  piston  through  the  piston- 
rod  E.  to  the  crank  G,  and  by  this  means  the  shaft  A  is 
rotated.  Connected  with  the  shaft  by  means  of  the  crank  H 
is  a  rod  E'  which  connects  with  the  valve  V,  so  that,  as  the 
shaft  rotates,  the  valve  for  the  greater  part  of  its  stroke  is 
made  to  slide  to  and  fro,  in  a  direction  opposite  to  that  of 
the  motion  of  the  piston. 


310  MOLECULAR  DYNAMICS. 

The  shaft  carries  a  fly-wheel  W.  This  is  a  large,  heavy 
wheel,  having  the  larger  portion  of  its  mass  located  near 
its  circumference  ;  it  serves  as  a  reservoir  of  energy,  which 
is  needed  to  make  the  rotation  of  the  shaft  and  all  other 
machinery  connected  with  it  uniform,  so  that  sudden  changes 
of  velocity  resulting  from  sudden  changes  of  the  driving 
power  or  resistances  may  be  avoided.  By  means  of  a  belt 
passing  over  the  wheel  W  motion  may  be  communicated 
from  the  shaft  to  any  machinery  desirable. 

268.  Condensing  and  non-condensing-engines.1  —  Sometimes 
steam,  after  it  has  done  its  work  in  the  cylinder,  is  conducted 
through  the  exhaust-pipe  to  a  chamber  Q,  called  a  condenser, 
where,  by.  means  of  a  spray  of  cold  water  introduced  through 
a  pipe  T,  it  is   suddenly  condensed.     This   water  must  be 
pumped  out  of  the  condenser  by  a  special  pump,  called  tech- 
nically the  air-pump;  thus  a  partial  vacuum  is  maintained. 
Such  an  engine  is  called  a  condensing-engine.     Its  advantage 
is  obvious,  for  if  the  exhaust-pipe,  instead  of  opening  into  a 
condenser,  communicate  with  the  outside  air.  as  in  the  non- 
condensing  engine,  the  steam  is  obliged  to  move  the  piston 
constantly   against   a   resistance    arising    from    atmospheric 
pressure  of  15  pounds  for  every  square  inch  of  the  surface  of 
the  piston.     But  in  the  condensing  engine  a  large  portion  of 
the  pressure  on  the  exhaust  side  of  the  piston  is  removed  and 
an  equivalent  portion  of  the  pressure  on  the  steam  side  is 
utilized  and  made  to  do  useful  work.     In  well  proportioned 
condensing  apparatus  the  pressure  on  the  exhaust  side  may 
be  reduced  90  per  cent.,  so  that  the  moving  piston  instead  of 
working  against  a  resistance  of  15  Ibs.  meets  with  a  resistance 
of  only  1.5  Ibs.  per  square  inch. 

269.  Steam  gauge.  —  An  instrument  called  a  steam  gauge 
is  connected  with  the  boiler.     It  measures  the  excess  of  the 

1  The  terms,  low-pressure  and  high-pressure  engines,  are  not  distinctive  as  applied 
to  engines  of  the  present  day. 


COMPOUND  OR  DOUBLE-CYLINDER  ENGINE. 


311 


pressure  of  the  steam  at  any  instant  above  the  atmospheric 
pressure.  The  absolute  pressure  of  the  steam  (i.e.  measured 
from  zero)  is  the  pressure  indicated  by  the  steam  gauge  plus 
the  pressure  of  the  atmosphere  at  the  time. 

270.  Compound  condensing  or  double-cylinder  engine.  —  This 
engine  has  two  cylinders,  each  like  that  of  a  simple  engine. 
One,  A  (Fig.  223),  called  the  high-pressure  cylinder,  receives 
steam  of  very  high  pressure  directly  from  the  boiler  through 


FIG.  223. 

the  orifice  V.  The  steam,  after  it  has  done  work  in  this 
cylinder,  passes  through  the  steam-port  E  into  cylinder  B, 
called  the  low-pressure  cylinder.  Cylinder  B  is  larger  than 
cylinder  A.  The  steam  which  enters  cylinder  B  possesses 
considerable  pressure,  and  is  therefore  capable  of  doing  con- 
siderable work  under  suitable  conditions.  It  should  be  borne 
in  mind  that  in  order  that  steam  may  do  work  in  any  cylinder, 
it  is  necessary  that  an  inequality  in  the  pressure  of  the  steam 


312  MOLECULAR    DYNAMICS. 

each  side  of  the  piston  should  be  maintained  ;  just  as  an 
inequality  of  level,  i.e.  a  head,  is  essential  to  water-power. 
The  steam,  after  it  has  done  its  work  in  cylinder  B,  passes 
through  a  port  C  into  a  condenser  (not  represented  in  the 
figure),  where  it  is  suddenly  condensed  or  let  down  to  a  very 
low  pressure.  If  a  vertical  glass  tube  were  led  from  the  con- 
denser to  a  vessel  of  mercury  below,  the  mercury  would 
ordinarily  stand  about  25  inches  high  in  the  tube,  which 
would  show  that  the  pressure  of  the  steam  against  which  the 
steam  when  it  enters  cylinder  B  does  work,  is  only  about 
one-sixth  of  an  atmosphere.  Much  energy  is  economized  by 
the  compound  engine. 

271.  The  locomotive.  —  The  distinctive  feature  of  the  loco- 
motive engine  is  its  great  steam-generating  capacity  relatively 
to  its  size  and  weight,  which  are  necessarily  limited.  To  do 
the  work  ordinarily  required  of  it,  from  three  to  six  tons  of 
water  must  be  converted  into  steam  per  hour.  This  is 
accomplished  in  two  ways :  first,  by  a  rapid  combustion  of 
fuel  (from  a  quarter  of  a  ton  to  a  ton  of  coal  per  hour); 
second,  by  bringing  the  water  in  contact  with  a  large  extent 
(about  800  square  feet)  of  heated  surface.  The  lire  in  the 
"  fire-box  "  A  (Plate  II)  is  made  to  burn  briskly  by  means  of  a 
powerful  draft  which  is  created  in  the  following  manner: 
The  exhaust  steam,  after  it  has  done  its  work  in  the  cylinders 
B,  is  conducted  by  tiie  exhaust-pipe  C  to  the  smoke-box  D, 
just  beneath  the  smoke-stack  E.  The  steam,  as  it  escapes 
from  the  blast-pipe  E,  pushes  the  air  above  it,  and  drags  by 
friction  the  air  around  it,  and  thus  produces  a  partial  vacuum 
in  the  smoke-box.  The  external  pressure  of  the  atmosphere 
then  forces  the  air  through  the  furnace  grate  and  hot-air 
tubes  (r,  and  thus  causes  a  constant  draft.  The  large  extent 
of  heated  surface  is  secured  as  follows  :  The  water  of  the 
boiler  is  brought  not  only  in  contact  with  the  heated  surface 
of  the  fire-box,  but  it  surrounds  the  pipes  G  (a  boiler  usually 


314  MOLECULAR    DYNAMICS. 

9.  Find  the  resulting  temperature  (C.)  of  the  following  mixtures:  — 

a.  5  K  of  snow  at  0°  with  25  K  of  water  at  28°. 
6.  4  K  of  ice  at  —  10°  with  30  K  of  water  at  50°. 
ic.  10  K  of  iron  at  200°  with  2  K  of  ice  at  0°. 

10.  How  many  thermal  units  are  required  to  change  5  K  of  ice  at 
—  10°  C.  into  water  at  10°  ? 

11.  If  30  g  of  steam  at  100°  C.  be  passed  into  400  g  of  ice-water  at 
0°  C.,  what  will  be  the  temperature  of  the  mixture  ? 

12.  A  building  is  heated  by  hot-water  pipes.     How  does  heat  get  from 
the  furnace  of  the  boiler  to  a  person  in  the  building  ? 

13.  A  building  is  heated  by  steam  pipes.     How  does  heat  get  from  the 
furnace  to  objects  in  the  building  ? 

» 14.  A  rod  of  copper  at  0°  C.  measures  10  ft. ;  its  length  at  100°  C.  is 
0.191  inch  greater.  Find  the  coefficient  of  expansion  of  copper. 

'  15.    A  silver  rod  at  0°  C.  is  10  ft.  long  ;  find  its  length  at  100°  C. 

16.  A  cubic  meter  of  air  at  100°  C.  is  cooled  down  to  0°,  and  at  the 
same  time  its  pressure  is  halved ;  determine  its  new  volume. 

» 17.  A  copper  ball  weighing  3  K,  taken  out  of  a  furnace  and  plunged 
into  8  k  of  water  at  10°  C.,  heated  the  water  to  25°  ;  find  the  temperature 
of  the  furnace.  Lf  V  ^ 

18.  If  the  heat  yielded  by  1  K  of  water  in  cooling  down  from  100°  to 
0°C.  were  employed  in  heating  10  K  of  mercury,  initially  at  20°,  to  what 
temperature  would  the  mercury  be  raised  ? 

>19.  A  kilogram  of  ice  at  0°C.  is  thrown  into  6.3  K  of  water  at  15°; 
when  the  ice  is  melted,  the  temperature  of  the  water  is  2°.  Find  the 
heat  of  fusion  of  ice. 

^  20.  A  mass  of  93.3  g  of  copper  at  80°  C.  is  immersed  in  560  g.  of  water 
at  10°,  arid  raises  the  temperature  of  the  water  to  20° ;  find  the  specific 
heat  of  copper. 


PART   III. 

ETHER  DYNAMICS. 


CHAPTER   I. 

ENERGY   OF   ETHER-STRAIN.      RADIANT   ENERGY.      LIGHT. 

SECTION  I. 

INTRODUCTION. 

OWING  to  the  peculiarity  of  the  subject  to  be  treated  in 
this,  the  third  and  final  natural  division  of  Physics,  it  is 
deemed  expedient  to  state  at  the  outset  some  leading  proposi- 
tions, whose  truth  must  be  assumed  as  the  basis  for  the  study 
of  a  large  group  of  natural  phenomena.  The  demonstrations 
of  the  validity  of  these  several  assumptions  must,  however, 
be  deferred  to  their  proper  place  in  connection  with  the  study 
of  the  phenomena  themselves. 

273.  The  ether.  —  We  know  matter  by  its  properties  as 
perceived  by  means  of  our  senses ;  in  other  words  the  exist- 
ence of  any  form  of  matter  is  to  us  only  an  inference  from 
the  phenomena  to  which  it  gives  rise.  By  evidence  of  pre- 
cisely similar  nature  are  we  led  to  believe  in  the  existence  of 
a  medium  called  the  ether,  pervading  all  space  and  penetrating 
between  the  molecules  of  matter,  which  are  imbedded  in  it 
and  surrounded  by  it  as  the  earth  is  surrounded  by  its  atmos- 
phere. We  cannot  see,  hear,  feel,  taste,  smell,  exhaust,  weigh, 
or  measure  it,  and  yet  all  this,  paradoxical  as  it  may  seem, 


316  ETHER    DYNAMICS. 

furnishes  absolutely  no  evidence  that  it  does  not  exist.  Briefly 
stated,  the  proof  of  its  existence  is  this :  it  furnishes  the 
basis  for  the  sole  conceivable  explanation  of  very  many  physical 
phenomena. 

Phenomena  occur  just  as  they  would  occur  -(/"all  space  were 
filled  with  an  intangible  and  invisible  medium  capable  of 
transmitting  motion  and  energy,  and  we  can  account  for  all 
these  phenomena  on  no  other  hypothesis  ;  hence  our  belief  in 
the  existence  of  the  medium.  The  evidence  of  the  existence 
of  ether  is  as  strong  and  direct  as  that  of  the  existence  of 
air.  The  eye  is  an  ether  sense-organ  just  as  the  ear  may  be 
called  an  air  sense-organ,  or  the  hand  a  sense-organ  for  the 
appreciation  of  grosser  forms  of  matter.1  The  ether  is  a 
medium  for  the  transmission  of  energy  in  the  form,  of  vibrations. 

In  its  structure  the  ether  is  assumed  to  be  excessively  fine- 
grained, "Differing  from  water,  glass  and  metals  in  being 
very  much  more  finely  grained  in  its  structure  " 2  (Lord  Kelvin). 
It  possesses  rigidity,3  and  in  this  respect  is  like  a  solid.  Bodies 
of  matter,  even  so  large  as  the  planets,  pass  freely  through  it, 
encountering  little  resistance  ;  therein  it  is  like  a  perfect 
fluid.  It  is  almost  perfectly  elastic  and  incompressible. 

274.  Radiation.  Radiant  energy.  —  The  transmission  of 
energy  by  means  of  periodic  disturbances  in  the  ether  is  called 
radiation;  energy  so  transmitted  is  called  radiant  energy; 

1  "  Instead  of  beginning  by  saying  that  we  know  nothing  about  the  ether,  I  say 
that  we  know  more  about  it  than  we  do  about  air  or  water,  glass  or  iron,  —  it  is  far 
simpler ;  there  is  far  less  to  know.    Its  natural  history  is  far  simpler  than  that  of 
any  other  body."  —  LORD  KELVIN,  in  lectures  on  Molecular  Dynamics  at  Johns 
Hopkins  University  (1884). 

2  "  The  ether  is  practically  a  homogeneous  solid,  — in  other  words  an  exceedingly 
fine-grained  solid,  so  finely  grained  that  it  is  practically  homogeneous  for  portions 
exceedingly  small  in  linear  dimensions  in  comparison  with  the  wave-length.    But  no 
degree  of  smallness  will  dispense  with  the  to  and  fro  motion  of  the  elastic  solid  rela- 
tively to  the  imbedded  molecules." 

8  Calculation  leads  us  to  infer  that  its  rigidity  is  about  10-9  that  of  steel,  and  its 
density  936  x  10~21  that  of  water  at  4°C.,  or  equal  to  that  of  our  atmosphere  at  a  hight 
of  210  miles,  —  a  density  vastly  greater  than  that  of  the  same  atmosphere  in  the 
interstellar  spaces.  — MAXWELL, 


EFFECTS    OF    RADIANT    ENERGY.  317 

and  the  body  emitting  energy  in  this  manner  is  called  a 
radiator.  The  precise  nature  of  the  periodic  disturbances, 
whether  they  be  due  to  changes  of  position  in  the  ether,  or  to 
alternation  between  opposite  conditions  (e.g.  such  as  succes- 
sive local  states  of  strain  or  distortion  and  release  therefrom) 
is  unknown  to  us.  We  do  know,  however,  that  the  laws 
according  to  which  these  changes  take  place  are  those  of 
wave-motion.  Space  is  traversed  at  all  times  and  in  all  direc- 
tions by  myriads  of  ether-waves  of  all  possible  lengths.  The 
all-pervading  ether  can  be  set  in  vibration  by  the  motion  of  the 
molecules  of  ordinary  matter.  This  local  disturbance  creates 
ether-waves,  and  by  these  waves  energy  is  transferred  from 
place  to  place  by  the  process,  as  stated  above,  called  radia- 
tion. Radiant  energy  can  be  transformed  into  any  other 
form  of  energy,  and  therefore  offers  no  exception  to  the  doc- 
trine of  correlation  of  energy. 

Just  how  vibrations  of  particles  of  matter  create  ether- 
waves,  and  what  constitutes  a  wave  of  ether,  are  things  of 
which  our  knowledge  is  as  yet  very  deficient.  It  must  be 
remembered  that  ether  is  a  substance  very  unlike  ordinary 
matter,  and,  therefore,  reasoning  by  analogy  must  often  fail. 
It  is  generally  supposed  that  ether-waves  are  not  waves  of 
compression  and  rarefaction,  like  those  of  sound-waves  in  air. 

Furthermore,  the  vibrations  which  occur  in  the  ether  are 
not  longitudinal  like  those  of  the  air  particles  during  the 
passage  of  sound-waves,  but  are  transversal  and  somewhat 
analogous  to  the  motions  of  particles  of  water  in  water-waves. 
That  is,  the  vibrations  in  ether  are  at  right  angles  to  the 
direction  in  which  the  wave  is  propagated,  and  are  therefore 
parallel  to  the  wave-front. 

275.  Effects  of  radiant  energy.  —  When  radiant  energy  is 
received  upon  the  surfaces  of  our  bodies,  warmth  is  felt ;  when 
upon  the  bulb  of  a  thermometer,  rise  of  temperature  is  indi- 
cated ;  when  by  the  eye,  the  sense  of  sight  may  be  affected  ; 


318  ETHER    DYNAMICS. 

if,  upon  sensitive  photographic  plates,  upon  the  leaves  of 
plants,  and  upon  various  chemical  mixtures,  chemical  changes 
may  be  promoted.  Thus  it  seems  that  when  ether-waves 
impinge  upon  objects  their  energy  is  transformed,  producing 
effects  of  different  kinds,  which  are  determined  by  the  nature 
of  the  body  upon  which  they  fall.  The  effect  which  most 
concerns  us  is  that  produced  when  the  radiations  strike  the 
eye  and  become  the  means,  through  this  organ,  of  awakening 
in  the  brain  the  sensation  which  we  call  Light. 


SECTION  II. 

LIGHT. 

276.  Light  defined.  Hypotheses.  —  Physiologically  speak- 
ing, light  is  the  sensation  of  sight.  Physically  considered,  it 
is  that  agent  ivhich,  by  its  action  on  the  retina  of  the  eye,  excites 
in  us  the  sensation  of  vision.  Two  leading  hypotheses  1  regard- 
ing the  nature  of  light  have  been  propounded,  which  are 
totally  different  in  character.  One  is  the  so-called  emission  or 
corpuscular  hypothesis  which  was  supported  by  Descartes 
(1629),  Newton  (1672),  and  most  physicists  up  to  the  early 
part  of  the  present  century.  It  assumes  that  a  luminous 
body  (e.g.  the  sun)  emits  minute  material  particles  (cor- 
puscles) which  travel  through  space  in  all  directions  with 
immense  velocity ;  these  particles  by  their  impact  upon  the 
nerve-woven  retina  produce  the  sensation  of  sight.  As  a 
rose  emits  minute  particles  which,  reaching  the  nostrils, 
enable  us  to  smell  the  rose,  so  a  star  is  supposed  to  emit  par- 

1  The  Platonists  maintained  that  the  sensation  of  light  was  produced  and  vision 
effected  hy  something  which  was  emitted  from  the  eye  to  the  object,  and  the  sense  of 
vision  was  explained  hy  the  analogy  of  touch.  "  The  light  from  the  sun,  the  twink- 
ling of  the  stars,  t"he  colors  of  the  rainbow,  and  the  various  hues  of  the  floor  of 
nature  remain  the  same  as  when  they  gladdened  the  heart  of  Noah  ;  but  how  have 
the  explanations  of  the  phenomena  varied  !  " 


LUMINOUS    AND   ILLUMINATED    OBJECTS.  319 

tides  of  light  which,  on  reaching  the  eye,  enable  us  to  see 
the  star. 

This  hypothesis  is  now  discarded  by  scientists  ;  the  reasons 
for  its  abandonment  will  appear  further  on.  The  theory 
which  obtains  at  the  present  time,  called  the  undulatory  or 
wave-theory,1  is  based  upon  the  hypothesis  that  energy  is 
transmitted  from  body  to  body,  e.g.  from  the  sun  to  the  earth 
(and  the  reverse),  in  the  form  of  vibrations  or  wave-action  in 
the  all-pervading  ether.  In  this  connection  it  should  be 
borne  in  mind  that  the  evidence  of  the  correctness  of  any 
theory  is  its  exclusive  competence  to  explain  and  coordinate 
phenomena.  It  is  not  claimed  that  all  phenomena  have  been 
fully  explained  by  the  wave  theory ;  it  is  merely  claimed 
that  all  we  know  at  the  present  time  about  light  is  in  perfect 
accord  with  it.  It  will  be  observed  that  both  theories  recog- 
nize the  fact  that  light  is  essentially  dynamic.  According  to 
the  latter  theory,  light  is  that  vibration  of  the  ether  which  may 
be  appreciated  by  the  organ  of  sight.12 

277.  Luminous  and  illuminated  objects.  —  Some  bodies  are 
seen  by  means  of  light-waves  which  they  generate  and  emit ; 
e.g.  the  sun,  a  candle  flame,  and  a  "  live  coal "  ;  they  are 
called  luminous  bodies.  Other  bodies  are  seen  only  by  means 
of  light-waves  which  they  receive  from  luminous  ones  and 
reflect  to  the  eye,  and,  when  thus  rendered  visible,  are  said  to 
be  illuminated ;  e.g.  the  moon,  a  man,  a  cloud,  and  a  "dead" 
coal. 

1  The  first  person  who  presented  the  wave-theory  of  light  in  a  definite  shape  was 
Huygens,  in  a  work  published  in  1690  under  the  title  of  Traite  de  la  Lumiere.    The 
theory  was  thoroughly  established  by  Young  and  Fresnel  between  the  years  1800  and 
1820. 

2  It  will  be  shown  further  on,  that  not  all  ether- waves  are  capable  of  affecting 
the  sight,  hence  for  the  purpose  of  distinction  we  apply  the  term  light-waves  to  those 
ether-Avaves  only  which  are  capable  of  producing  vision.    It  is  strongly  recommended 
that  the  student  in  beginning  this  branch  of  science  make  use  of  the  term  light-waves 
instead  of  light  except  when  such  usage  would  lead  to  an  inconvenient  circumlocu- 
tion, in  order  that  he  may  have  strongly  impressed  upon  his  mind  the  fact  that  when 
he  is  dealing  with  light  he  is  dealing  with  waves. 


320 


ETHER    DYNAMICS. 


278.  Light  itself  invisible.  —  Light  makes  visible  to  us 
luminous  or  illuminated  objects,  light-waves  from  which 
actually  reach  our  eyes  ;  but  if  we  look  across  the  line  of 
direction  of  a  series  of  light-waves,  termed  the  path  of  the 
light,  we  cannot  see  the  light.  If  we  appear  to  see  a  sun- 
beam admitted  through  a  key-hole  or  knot-hole,  and  travers- 
ing a  darkened  room,  it  is  only  because  it  is  made  to  reveal  its 
track  by  illuminating  the  dust  motes  floating  in  the  air.  If 
the  air  in  a  certain  space  be  cleansed  of  dust,  the  path  of  a 
sunbeam  through  the  space  will  be  totally  imperceptible.1 

279.  Light-waves  travel  in  straight 
lines.  —  The  path  of  light-waves   ad- 
mitted into  a  darkened  room  through 
a  small  aperture,  as  indicated  by  the 
illuminated  dust,  is  perfectly  straight. 
An  object  is  seen   by  means   of  light- 
waves which  it  sends  to  the  eye.    A  small 
object  placed  in  a  straight  line  between 
the  eye  and  a  luminous  point  may  in- 
tercept the  light-waves  in  that  path, 
and  the  point  become  invisible.    Hence 
we   cannot   see   around   a   corner,   or 
through  a  bent  tube. 

280.  Ray,  beam,  pencil.  —  Any  line 
RR  (Fig.  224)  which  pierces  the  surface 
of  an  ether-wave  ab  perpendicularly,  is 
called  a  ray.     The  term  "  ray  "  is  but 

an  expression  for  the  direction  in  which  motion  is  propagated, 
and  along  which  the  successive  effects  of  ether-waves  occur?  If 
the  wave-surface  a'b'  be  a  plane,  the  rays  R'R'  are  parallel, 

1  See  Tyndall's  Fragments  of  Science,  p.  277. 

2  In  dealing  with  certain  phenomena  (e.g.  reflection  of  light)  we  may,  to  facilitate 
our  study,  consider  the  light  as  propagated  in  straight  lines  or  rays ;  but  we  must 
bear  in  mind  that  a  ray  has  no  material  or  physical  existence,  for  it  is  a  wave  that 
is  propagated,  not  a  ray. 


TRANSPARENT    AND    OPAQUE    SUBSTANCES.          321 

and  a  collection  of  such  rays  is  called  a  beam.  If  the  wave- 
surface  a"b"  be  spherical,  the  rays  R"R"  have  a  common  point 
at  the  center  of  curvature  ;  and  a  collection  of  such  rays  is 
called  a  pencil. 

281.  Transparent)  translucent,  and  opaque  substances.  —  Sub- 
stances are  transparent,  translucent,  or   opaque,  according  to 
the  manner  in  which  they  act  upon   the  light-waves  which 
are    incident   upon   them.      Generally   speaking,    those    sub- 
stances are  transparent  that  allow  other  objects  to  be  seen 
through  them  distinctly,  e.g.  air,  glass,  and  water.      Those 
substances  are  translucent  that  allow  light-waves  to  pass,  but 
in  such  a  scattered  condition  that  objects  are  not  seen  dis- 
tinctly through  them,  e.g.  fog,  ground  glass,  and  oiled  paper. 
Those  substances  are  opaque  .that  apparently  cut  off  all  the 
light-waves    and   prevent   objects   from   being  seen  through 
them.       When  bodies  intercept  light,  they  are  said  to  cast 
shadows. 

282.  Every  point  of  a  luminous  body  an  independent  source 
of  liyht-waves.  —  Place   a  candle   flame   in  the    center  of   a 
darkened   room ;    each  wall   and   every   point  of   each  wall 
becomes  illuminated.    Place  your- 
self in  any  part  of  the  room,  i.e. 

in  any  direction  from  the  flame ; 

you  are  able  to  see  not  only  the 

flame,    but    every    point    of    the 

flame ;  hence  every  point  of  the 

flame   must   emit  light-waves  in 

every  direction.     Every  point  of 

a  luminous  body  is  an  Independent 

source  of  light-waves,   and  emits 

them  in  every  direction.     Such  a 

point  is  called  a  luminous  point. 

In  Figure  225  there  are   represented  a  few  of  the  infinite 

number  of  pencils  of  light  emitted  by  three  luminous  points 


322 


ETHER    DYNAMICS. 


of  a  candle  flame.     Every  point  of  an  illuminated  object  ab 
receives  light  from  every  luminous  point. 
283.    Images  formed  through  small  apertures. 

Experiment  1.  —  Cut  a  hole  about  8cm  square  in  one  side  of  a  box ; 
cover  the  hole  with  tin-foil,  and  prick  a  hole  in  the  foil  with  a  pin. 
Place  the  box  in  a  darkened  room,  and  a  candle  flame  in  the  box  near 
the  pin  hole.  Hold  an  oiled-paper  screen  before  the  hole  in  the  foil ;  an 
inverted  image  of  the  candle  flame  will  appear  upon  the  translucent 
paper.  An  image  is  a  kind  of  picture  of  an  object. 

If  light-waves  from  objects  illuminated  by  the  sun  —  e.g. 
trees,  houses,  clouds,  or  even  an  entire  landscape  —  be  allowed 
to  pass  through  a  small  aperture  in  a  window  shutter  and  strike 
a  white  screen  (or  a  white  wall)  in  a  dark  room,  inverted  images 
of  the  objects  in  their  true  colors  will  appear  upon  the  screen. 
The  cause  of  these  phenomena  is  easily  understood.  When  no 

screen  intervenes  between  the 
candle  and  the  screen  A  (Fig. 
226),  every  point  of  the  screen 
receives  light  from  every  point 
of  the  candle;  consequently, 
at  every  point  on  A,  images  of 
the  infinite  number  of  points 
of  the  candle  are  formed.  The 
result  of  the  confusion  of 
images  is  that  no  image  is  distinguishable.  But  let  the  screen 
B,  containing  a  small  hole,  be  interposed  ;  then,  since  light 
travels  only  in  straight  lines,  the  point  Y'  can  receive  an 
image  only  of  the  point  Y,  the  point  Z'  only  of  the  point  Z, 
and  so  for  intermediate  points  ;  hence  a  distinct  image  of  the 
object  must  be  formed  on  the  screen  A.  That  an  image  may 
be  distinct,  the  images  of  different  points  of  the  object  must  not 
mix,  and  therefore  all  rays  from  each  point  on  the  object  must 
be  carried  to  the  corresponding  point  on  the  image. 


FIG.  226. 


SHADOWS.  328 

The  brightness  of  the  image  decreases  as  the  opening  is 
made  smaller,  since  less  light  can  pass  through  it.  The 
aperture,  if  small,  may  have  any  shape  without  affecting 
the  outline  of  the  image.  The  image  of  the  sun  is  a  circle, 
irrespective  of  the  shape  of  the  aperture,  if  its  rays  strike 
the  screen  perpendicularly ;  but  elliptical,  if  they  strike  the 
screen  obliquely. 

284.    Shadows. 

Experiment  2.  —  Procure  two  pieces  of  tin  or  cardboard,  one  18cm 
square,  the  other  3cm  square.  Place  the  first  between  a  white  wall  and 
a  candle  flame  in  a  darkened  room.  The  opaque  tin  intercepts  the  light 
that  strikes  it,  and  thereby  excludes  light  from  a  space  behind  it. 

This  space  is  called  a  shadow.  That  portion  of  the  surface 
of  the  wall  that  is  darkened  is  a  section  of  the  shadow,  and 
represents  in  form  a  cross  section  of  the  body  that  intercepts 
the  light.  A  section  of  a  shadow  is  frequently  for  conven- 
ience called  a  shadow.  Notice  that  the  shadow  is  made  up 
of  two  distinct  parts,  —  a  dark  center  bordered  on  all  sides 
by  a  much  lighter  fringe.  The  dark  center  is  called  the 
umbra,  and  the  lighter  envelope  is  called  the  penumbra. 

Experiment  3. — Carry  the  tin  nearer  the  wall,  and  notice  that  the 
penumbra  gradually  disappears  and  the  outline  of  the  umbra  becomes 
more  distinct.  Employ  two  candle  flames,  a  little  distance  apart,  and 
notice  that  two  shadows  are  produced.  Move  the  tin  toward  the  wall, 
and  the  two  shadows  approach  each  other,  then  touch,  and  finally  over- 
lap. Notice  that  where  they  overlap  the  shadow  is  deepest.  This  part 
gets  no  light  from  either  flame,  and  is  the  umbra ;  while  the  remaining 
portion  gets  light  from  one  or  the  other,  and  is  the  penumbra. 

Just  so  the  umbra  of  every  shadow  is  the  part  that  gets  no 
light  from  the  luminous  body,  while  the  penumbra  is  the  part 
that  gets  light  from  some  portion  of  the  body,  but  not  from  the 
whole. 


324 


ETHER    DYNAMICS. 


Experiment  4.  —  Repeat  the  above  experiments,  employing  the  smaller 
piece  of  tin,  and  note  all  differences  in  phenomena  that  occur.  Hold  a 
hair  in  the  sunlight,  about  a  centimeter  in  front  of  a  fly-leaf  of  this  book, 

and  observe  the  shadow  cast  by  the 
hair.  Then  gradually  increase  the  dis- 
tance between  the  hair  and  the  leaf, 
and  note  the  change  of  phenomena. 

If  the  source  of  light  were  a  single 
luminous  point,   as  A   (Fig.   227),    the 

shadow  of  an  opaque  body  B  would  be  of  infinite  length,  and  would  con- 
sist only  of  an  umbra.  But,  if  the  source  of  light  have  a  sensible  size, 
the  opaque  body  will  intercept  just  as  many  separate  pencils  of  light  as 
there  are  luminous  points,  and  consequently  will  cast  an  equal  number  of 
independent  shadows. 

Let  A  B  (Fig.  228)  represent  a  luminous  body,  and  C  D  an  opaque 
body.  The  pencil  from  the  luminous  point  A  will  be  intercepted  between 


FIG.  2-J7. 


the  lines  C  F  and  D  G,  and  the  pencil  from  B  will  be  intercepted  between 
the  lines  C  E  and  D  F.  Hence,  the  light  will  be  wholly  excluded  only 
from  the  space  between  the  lines  C  F  and  D  F,  which  enclose  the  umbra. 
The  enveloping  penumbra,  a  section  of  which  is  included  between  the 
lines  C  E  and  C  F,  and  between  D  F  and  D  G,  receives  light  from  certain 
points  of  the  luminous  body,  but  not  from  all. 


LIGHT    REQUIRES    TIME    TO    PASS    THROUGH    SPACE.    325 


Questions. 

1.  Why  are  images  formed  through  apertures  inverted  ? 

2.  Why  is  the  size  of  the  image  dependent  on  the  distance  of  the 
screen  from  the  aperture  ? 

3.  Why-  does  an  image  become  dimmer  as  it  becomes  larger  ? 

4.  Why  do  we  not  imprint  an  image  of  our  person  on  every  object  in 
front  of  which  we  stand  ? 

5.  Upon  what  fact  does  a  gunner  rely  in  taking  sight  ? 

6.  Explain  the  umbra  and  penumbra  cast  by  the  opaque  body  H  I, 
Fig.  228. 

7.  When  will  a  transverse  section  of  the  umbra  of  an  opaque  body  be 
larger  than  the  object  itself  ? 

8.  When  has  an  umbra  a  limited  length  ? 

9.  What  is  the  shape  of  the  umbra  cast  by  the  sphere  C  D,  Fig.  228  ? 

10.  If  C  D  should  become  the  luminous  body,  and  A  B  a  non-luminous 
opaque  body,  what  changes  would  occur  in  the  umbra  and  the  shadow 
cast? 

11.  Why  is  it  difficult  to  determine  the  exact  point  on  the  ground 
where  the  umbra  of  a  church-steeple  terminates  ? 

12.  What  is  the  shape  of  a  section  of  the  shadow  cast  by  a  circular 
disk  placed  obliquely  between  a  luminous  body  and  a  screen  ?     What  is 
its  shape  when  the  disk  is  placed  edgewise  ? 

13.  The  section  of  the  earth's  umbra  on  the  moon  in  an  eclipse  always 
has  a  circular  outline.     What  does  this  show  respecting  the  shape  of  the 
earth  ? 

14.  Describe  the  shadow  cast  by  the  earth. 

15.  Why  does  the  electric  arc  lamp  cast  well  defined  shadows  ? 


SECTION   III. 

SPEED    OF    LIGHT. 

285.  Light  requires  time  to  pass  through  space.  —  That  light 
travels  with  finite  speed  was  first  established  in  1676  by  the 
Danish  astronomer  Olaf  Roemer,  then  engaged  in  Paris  in 
observing  the  eclipses  of  Jupiter's  moons.  He  made  obser- 


326  ETHEK    DYNAMICS. 

vations  on  that  one  of  the  five  of  Jupiter's  satellites  which 
is  nearest  to  the  planet,  and  which  revolves  round  this  planet 
as  the  moon  does  round  the  earth.  At  regular  intervals  the 
satellite  passes  behind  the  planet  and  is  eclipsed  within  its 
shadow.  The  observed  intervals,  however,  were  found  to  be 
shorter  than  the  mean  value  when  the  Earth  and  Jupiter. 
were  approaching  each  other,  and  longer  when  they  were 
receding  from  each  other.  It  was  evident  that  this  difference 
was  due  to  the  time  consumed  by  the  light  in  crossing  the 
intervening  spaces.  From  the  results  of  these  observations 
it  was  calculated  that  light  required  16  minutes  and  36 
seconds  to  traverse  the  diameter  of  the  earth's  orbit,  approxi- 
mately 185,000,000  miles. 

It  was  then  an  easy  matter  for  Koemer  to  determine  how 
far  light  travels  per  second.  The  speed  of  light  as  deter- 
mined by  Eoemer  is  192,500  miles  per  second.  It  has  been 
determined  by  later  experiments  and  more  reliable  methods 
that  this  estimate  is  too  great.  The  result  obtained  by 
Michelson  at  Cleveland  (1882)  is  299,853  kilometers  (=  about 
186,380  miles)  per  second.  This  may  be  accepted  as  probably 
the  nearest  approximation  yet  made  to  the  true  speed  of  light 
in  a  vacuum.  At  this  rate,  light  would  encircle  our  earth 
between  seven  and  eight  times  in  a  second. 

Sound  creeps  along  at  the  comparatively  slow  pace  of  about 
one-fifth  of  a  mile  (or  -J-Km)  per  second.  The  former  is  the 
speed  with  which  waves  in  ether  are  transmitted ;  the  latter, 
the  speed  with  which  waves  in  air  move  forward.  This  great 
difference  can  be  accounted  for  only  on  the  supposition  that 
the  ether  is  far  less  dense  and  much  more  elastic  than  air. 

Notwithstanding  its  great  speed,  light  requires  no  less 
than  three  years  to  reach  us  from  the  nearest  fixed  star 
(a  Centauri),  and  from  those  more  distant  it  requires  cen- 
turies. It  is  thus  possible,  through  the  instrumentality  of 
light,  faintly  to  conceive  of  the  vastness  of  space. 


UNIT   OF   MEASUREMENT.  327 


SECTION  IV. 

INTENSITY    OF    ILLUMINATION. 

286.  Unit  of  measurement.  —  The  unit  generally  employed 
for  the  measurement  of  the  intensity  of  the  light  emitted  by 
a  luminous  body  is  the  British  candle  power.1     It  is  the  in- 
tensity of  light  emitted  by  a  sperm  candle  -J  in.  in  diameter, 
burning  120  grains  to  the  hour. 

287.  Diminution  of  intensity  of  illuminating  capacity  with 
distance.     Application  of  the  law  of  inverse  squares  to  light. 
—  Light  diminishes  in  intensity,  and  hence  in  its  power  to 
illuminate  objects  which  it  strikes,  as  it  recedes  from  its 
source.      The  intensity  of  light  diminishes  as  the  square  of  the 
distance  from  its  source  increases.      Calling  the  quantity  of 
light  falling  upon  a  visiting  card  at  a  distance  of  2  feet  from 
a  lamp  flame  1,  the  quantity  falling  upon  the  same  card  at  a 
distance  of  4  feet  is  J,  at  a  distance  of  6  feet  it  is  £,  and  so 
on.     This  is  the  meaning  of  the  law  of  inverse  squares,  as 
applied  to  light. 

1  The  French  unit  is  the  carcel  (the  name  given  to  a  lamp),  which  is  equal  to  9£ 
candles.  The  unit  adopted  at  the  International  Congress  of  Electricians  in  1884  is 
the  light  emitted  by  a  square  centimeter  of  molten  platinum  at  the  temperature  of 
solidification,  or  about  2.08  carcels,  or  19.8  candles.  This  is  called  the  platinum 
standard  ;  and  the  method,  the  Violle  method.  Subsequently  (1889),  ^  of  this  unit 
was  adopted  as  the  practical  standard. 

"  By  photometric  methods  it  is  found  that  the  sun  gives  us  1575  billions  of  billions 
times  as  much  light  as  a  standard  candle  would  do  at  that  distance. 

"  The  intensity  of  sunlight,  or  the  intrinsic  brightness  of  the  sun's  surface,  is 
quite  a  different  matter  from  the  total  quantity  of  its  light  expressed  in  candle 
power.  By  intensity  we  mean  the  amount  of  light  per  square  unit  of  luminous 
surface.  From  the  best  data  we  can  get  we  find  that  the  sun's  surface  is  about 
190,000  times  as  bright  as  that  of  a  candle  flame ;  and  about  150  times  as  bright  as 
the  lime  of  a  calcium  light. 

"  The  brightest  part  of  an  electric  arc  comes  nearer  sunlight  in  intensity  than 
anything  else  that  we  know,  being  from  one-half  to  one-quarter  as  bright  as  the  solar 
surface  itself." —  Young' 's  Elements  of  Astronomy. 

"  If  there  were  an  electric  light  of  2000-candle  power  on  each  square  foot  of  the 
surface  of  the  earth,  the  whole  light  from  the  earth  would  be  less  than  one  billionth 
that  from  the  sun."  — L ANGLE v.  The  earth  intercepts  an  extremely  small  part  of 
the  whole  quantity  of  light  emitted  by  the  sun. 


328 


ETHER    DYNAMICS. 


FIG.  229. 


This  law  may  be  illustrated  thus  :  A  square  card  placed 
(say)  1  foot  from  a  certain  point  in  a  candle  flame,  as  at  A 
(Fig.  229),  receives  from  this  point  a 
certain  quantity  of  light.  The  same 
light  if  not  intercepted  would  go  on  to 
B,  at  a  distance  of  2  feet,  and  would 
there  illuminate  four  squares,  each  of 
the  size  of  the  card,  and  being  spread 
over  four  times  the  area  can  illuminate 

each  square  with  only  one  fourth  the  intensity.  If  allowed 
to  proceed  to  C,  3  feet  distant,  it  illuminates  nine  such 
squares,  arid  has  but  one  ninth  its  intensity  at  A.  The  law 
is  strictly  true  only  when  distance  from  individual  points  is 
considered. 

288.  Photometry.  —  The  law  just  established  enables  us  to 
compare  the  illuminating  power  of  one  light  with  that  of  an- 
other, and  to  express  by  numbers  their  relative  illuminating 
powers.  The  process  is  called  photometry  (light-measuring) ; 
and  the  instrument  employed,  a  photometer. 


FIG.  230. 

289.  The  Bunsen  photometer  (Fig.  230)  has  a  screen  of 
paper,  S,  mounted  in  a  box,  B,  open  in  front  and  at  the 
two  ends.  The  box  slides  on  a  graduated  bar.  The  screen 
has  a  circular  central  spot  saturated  with  paraffine,  which 
renders  the  spot  more  translucent  than  other  portions  of  the 
screen.  One  side  of  the  screen  is  illuminated  by  the  light, 
L,  whose  intensity  is  to  be  measured,  and  the  other  side  by 


THE    BTJNSEN    PHOTOMETER. 


329 


171  "" 

\ 

2 

^-w' 

—  > 

•4  

s 

E         [ 
FIG.  23 

i. 

a  standard  candle,  L'.  When  the  screen  is  so  placed  that 
the  two  sides  are  equally  illuminated  by  the  two  lights,  the 
paraffined  spot  becomes  nearly  invisible.  When  one  side  is 
more  strongly  illuminated  than  the  other,  the  spot  appears 
dark  on  that  side  and  light  on  the  other.  The  candle  power 
of  the  two  lights  is  direcMy  proportional  to  the  square  of  their 
respective  distances  from 
the  screen  when  it  is 
equally  illuminated  on 
both  sides. 

In  order  to  render  both 
sides  of  the  disk  simul- 
taneously visible,  two 
mirrors,  m  and  m'  (Fig. 
231),  are  placed  in  the  box  in  a  vertical  position  so  as  to 
reflect  images  of  the  circular  spot  in  the  screen,  S,  to  the 
eyes  at  E  E!. 

Question?. 

1.  Suppose  that  a  lighted  candle  is  placed  in  the  center  of  each  of 
three  cubical  rooms,  respectively  10,  20,  and  30  feet  on  a  side ;  would  a 
single  wall  of  the  first  room  receive  more  light  than  a  single  wall  of  either 
of  the  other  rooms,  or  less  ? 

2.  Would  one  square  foot  of  a  wall  of  the  third  room  receive  as  much 
light  as  would  be  received  by  one  square  foot  of  a  wall  of  the  first  room  ? 
If  not,  what  difference  would  there  be,  and  why  the  difference  ? 

3.  If  a  board  10  cm  square  be  placed  25  cm  from  a  candle  flame,  the 
area  of  the  shadow  of  the  board  cast  on  a  screen  75  cm  distant  from  the 
candle  will  be  how  many  times  the  area  of  the  board  ?     Then  the  light 
intercepted  by  the  board  will  illuminate  how  much  of  the  surface  of  the 
screen  if  the  board  be  withdrawn  ? 

4.  Give  a  reason  for  the  law  of  inverse  squares. 

5.  To  what  besides  light  has  this  law  been  found  applicable  ? 

6.  The  two  sides  of  a  paper  disk  are  illuminated  equally  by  a  candle 
flame  50  cm  distant  on  one  side  and  a  gas  flame  200  cm  distant  on  the 
other  side.     a.  Compare  the  intensities  of  the  two  lights  at  equal  dis- 
tances from  their  sources.     6.  If  the  candle  be  a  standard  candle,  what 
is  the  intensity  of  the  gas  flame  ? 


330  ETHER   DYNAMICS. 


SECTION  V. 

APPARENT    SIZE    OF    AN    OBJECT. 

290.    Visual  angle. 

Experiment.  —  Prick  a  pin-hole  in  a  card,  place  an  eye  near  the  hole, 
and  look  at  a  pin  about  20  cm  distant.  Then  bring  the  pin  slowly  toward 
the  eye.  and  the  dimensions  of  the  pin  will  appear  to  increase  as  the  dis- 
tance diminishes. 

Why  is  this  ?  We  see  an  object  by  means  of  its  image 
formed  on  the  retina  of  the  eye  ;  and  its  apparent  magnitude 
is  determined  by  the  extent  of  the  retina  covered  by  its 
image.  Rays  proceeding  from  opposite  extremities  of  an 
object,  as  AB  (Fig.  232),  meet  and  cross  each  other  within 

A 


FIG.  232. 

the  eye.  Now,  as  the  distance  between  the  points  of  the 
blades  of  a  pair  of  scissors  depends  upon  the  angle  that  the 
handles  form  with  each  other,  so  the  size  of  the  image 
formed  on  the  retina  depends  upon  the  size  of  the  angle, 
called  the  visual  angle,  formed  by  these  rays  as  they  enter 
the  eye.  But  the  size  of  the  visual  angle  diminishes  approxi- 
mately as  the  distance  of  the  object  from  the  eye  increases, 
as  shown  in  the  diagram  ;  e.g.  at  twice  the  distance  the  angle 
is  about  one-half  as  great ;  at  three  times  the  distance  the 
angle  is  one-third  as  great ;  and  so  on.  Hence,  distance  affects 
the  apparent  size  of  an  object.  Our  judgment  of  the  size  of 
objects  is,  however,  influenced  by  other  things  besides  the 
visual  angle  which  they  subtend. 


MIRRORS.  331 

4 

SECTION  VI. 

REFLECTION    OF    LIGHT. 

291.  Mirrors.     Images.  —  Objects  having  polished  surfaces 
which  reflect  light  regularly  (i.e.  do  not  scatter  the  light), 
and  show  images   of  objects   presented  to  them,  are  called 
mirrors.     The  mirror  itself,  if  clean  and  smooth,  is  scarcely 
visible.     An  image  is  a  picture  of  an  object.     According  to 
their  shape  mirrors  are  called  plane,  concave,  convex,  spherical, 
parabolic,  etc. 

Experiment  1.  —  a.  Look  at  the  mirror  M  through  the  hole  marked  O 
in  the  metal  band  (Fig.  233).  You  see  in  the  mirror  an  image  of  the 
hole  through  which  you  look,  t 

but  you  do  not  see  the  image 
of  any  of  the  other  holes.  Rays 
that  pass  through  this  hole 
strike  the  mirror  perpendicu- 
larly and  are  said  to  be  normal 
to  the  mirror.  Rays  falling  FlG 

upon  an  object  are  called  inci- 
dent rays.  The  point  where  a  ray  strikes  is  called  the  point  of  incidence. 
The  reflected  rays  in  this  case  are  thrown  back  in  the  same  lines  and 
through  the  same  hole  that  the  incident  rays  travel.  Bays  normal  to  a 
mirror  after  reflection  simply  retrace  their  own  course,  b.  Next  hold  a 
candle  flame  at  one  of  the  other  holes,  e.g.  at  the  hole  marked  10.  You 
can  see  the  image  of  the  candle  flame  only  through  the  hole  of  the  same 
number  and  at  an  equal  distance  on  the  other  side.  The  angle  which  an 
incident  ray  makes  with  a  line  normal  at  the  point  of  incidence  is  called 
the  angle  of  incidence,  and  the  angle  made  by  a  reflected  ray  with  the 
normal  is  called  the  angle  of  reflection. 

LAW  OF  REFLECTION.  The  angles  of  incidence  and  reflec- 
tion are  in  the  same  plane,  and  are  equal. 

292.  The  wave-theory  applied  to  reflection. 

The  following  is  an  explanation  of  reflection  in  accordance  with 
the  wave-theory.  Suppose  KA,  ND,  etc.  (Fig.  234)  to  be  parallel 
rays  of  a  beam  of  light  falling  on  a  plane  mirror  HI. 


332 


ETHER    DYNAMICS. 


may  represent  the  plane  front  of  one  of  the  waves.  As  soon  as  the 
wave  reaches  A,  that  point  becomes  the  origin  of  a  disturbance  in 
the  ether,  which  spreads  out  in  the  form  of  a  sphere  having  its 
center  at  A.  This  disturbance  may  for  convenience  be  called  an 
undulation.  Let  the  arc  of  a  circle  described  around  A  as  a  center 
denote  the  boundary  which  the  undulation  has  reached  during  the 
interval  between  the  arrival  of  the  plane-wave  at  A  and  D  respec- 
tively ;  then  the  radius  of  this  circle  is  equal  to  the  excess  of  ND 


over  KA,  because  so  long  as  light  travels  in  the  same  isotropic 
medium  its  speed  in  all  directions  is  the  same.  Similarly  let  circles 
be  described  around  points  B,  C,  and  1)  with  radii  determined  in 
the  same  manner.  A  straight  line  a&cD,  drawn  tangent  to  these 
circles  at  the  points  a,  6,  etc. ,  represents  a  plane  reflected  wave-front 
corresponding  to  the  plane  incident- wave.  It  is  inclined  to  H I  at 
the  same  angle  but  in  the  opposite  direction  from  a  normal. 

293.    The  doubled  angle  of  reflection. 

When  a  mirror  is  rotated,  a  beam 
of  light  reflected  from  it  is  deflected 
through  an  angle  equal  to  twice  that 
of  the  rotation  of  the  mirror.  In  Fig. 
235,  I  M  is  an  incident  ray,  MR  a 
reflected  ray.  If  the  mirror  be  turned 
into  the  position  A'B',  the  reflected 
ray  is  now  M  R' ;  the  reflected  ray 
*  has  moved  through  the  angle  It  M  R', 
which  is  equal  to  twice  the  angle 
A  M  A'.  This  fact  suggests  an  invalu- 
able method  of  making  minute  motions 

apparent.  The  reflected  ray  itself  serving  as  a  weightless  index- 
pointer  of  any  desired  length,  and  capable  of  magnifying  motions  to 


INTENSITY    OF    REFLECTED    LIGHT.  333 

any  desired  extent.  For  example,  the  almost  imperceptible  motion 
of  the  pulse  may  be  made  visible  to  a  large  audience  in  the  follow- 
ing manner:  Lay  (or 
stick  with  wax)  a  tiny 
mirror  upon  the  throb- 
bing part  of  the  wrist. 
In  a  darkened  room 
project  from  a  lantern 
(or  porte-lumiere)  a 
small  beam  of  light 

obliquely     upon     the  FlG  236 

mirror  M  (Fig.  236), 

and  let  the  reflected  beam  strike  the  ceiling  above.    The  spot  of  light 
on  the  screen  will  move  several  inches  with  each  pulsation. 

294.  Intensity  of  reflected  light.  —  The  intensity  of  reflected 
light  increases  with  the  polish  of  the  reflecting  surface  and 
with  the  obliquity  of  the  incident  rays.      It  also  depends 
largely  upon  the  nature   of  the  medium  from  which   it  is 
reflected.      For  example,   at  perpendicular  incidence,   water 
reflects    about  the  fiftieth  part  of  the  incident   light  while 
mercury  reflects  about  two-thirds  ;    but  at  an   incidence  of 
89£°  each  reflects  about  72  per  cent  of  the   incident  light. 
The  varnished  surfaces   of  furniture  appear  much  brightei 
when  viewed  obliquely  than  when  seen  by  light  from  a  win- ' 
dow  reflected  less  obliquely.     Light  reflected  from  the  surface 
of  a  pond  just  before  the  sun  sets  is  much  more  dazzling  than 
at  noon  when  the  sun  is  overhead.     This  is  due  in  part  to 
the  fact  that  we  are  in  a  suitable  position  to  observe  it. 

295.  Diffused  light. 

Experiment  2.  —  Introduce  a  small  beam  of  light  into  a  darkened  room, 
by  means  of  a  porte-lumiere,  and  place  in  its  path  a  mirror.  The  light  is 
reflected  in  a  definite  direction.  If  the  eye  be  placed  so  as  to  receive  the 
reflected  light,  it  will  see,  not  the  mirror,  but  the  image  of  the  sun,  and 
the  light  will  be  painfully  intense.  Substitute  for  the  mirror  a  piece  of 
unglazed  paper.  The  light  is  not  reflected  by  the  paper  in  any  definite 
direction,  but  is  scattered  in  every  direction,  illuminating  objects  in  the 


334  ETHER    DYNAMICS. 

vicinity  and  rendering  them  visible.  Looking  at  the  paper,  you  see,  not 
an  image  of  the  sun,  but  the  paper,  and  you  may  see  it  equally  well  in 
all  directions. 

The  dull  surface  of  the  paper  receives  light  in  a  definite 
direction,  but  reflects  it  in  every  direction ;  in  other  words, 
it  scatters  or  diffuses  the  light.  The  difference  in  the  phe- 
nomena in  the  two  cases  is  caused  by  the  difference  in  the 
smoothness  of  the  two  reflecting  surfaces.  A  B  (Fig.  237) 
represents  a  smooth  surface,  like  that  of  glass,  which  reflects 
nearly  all  the  rays  of  light  in  the  same  direction,  because 
nearly  all  the  points  of  reflection  are  in  the  same  plane. 
C  D  represents  a  surface  of  paper  having  the  roughness  of 
its  surface  greatly  exaggerated.  The  various  points  of  re- 


flection are  turned  in  every  possible  direction ;  consequently, 
light  is  reflected  in  every  direction.  Thus,  the  dull  surfaces 
of  various  objects  around  us  reflect  light  in  all  directions, 
and  are  consequently  visible  from  every  side.  Objects  ren- 
dered visible  by  reflected  light  are  said  to  be  illuminated. 

By  means  of  regularly  reflected  light  we  see  images  of 
objects  in  mirrors,  but  only  from  definite  positions,  i.e.  in 
definite  directions ;  by  means  of  diffused  light  we  see  the 
object  itself  from  every  direction.  Whether  we  see  the  image 
of  the  source  of  the  light  (the  eye  being  situated  so  as  to 
receive  the  regularly  reflected  light),  or  the  object  on  which 
the  light  falls,  or  both  at  the  same  time,  depends  largely 
upon  the  degree  of  smoothness  possessed  by  the  surface  that 
reflects  the  light.  Polished  metals  are  the  best  mirrors. 
Surfaces  of  liquids  at  rest  are  excellent  mirrors.  It  is  some- 


REFLECTION  FROM  PLANE  MIRRORS.       335 

times  difficult  to  see  a  smooth  surface  of  a  pond  surrounded 
by  trees  and  overhung  by  clouds,  as  the  eye  is  occupied  by 
the  reflected  images  of  these  objects ;  but  a  faint  breath  of 
wind,  slightly  rippling  the  surface,  will  reveal  the  water. 

296.    Reflection  from  plane  mirrors  ;  virtual  images.  —  MM 
(Fig.  238)  represents  a  plane  mirror,  and  AB  a  pencil  of 
divergent    rays    proceeding    from    the 
point  A  of  an  object  A  H.     By  erect- 
ing   perpendiculars    at    the    points    of 
incidence,   or   the   points  where   these 
rays    strike   the    mirror,    and    making 
the  angles  of   reflection  equal  to  the 
angles  of  incidence,  the  paths  B  C  and 
E  C  of  the  reflected  rays  are  found. 

Every  visible  pojut  of  an  object 
sends  a  cone  of.  rays  to  the  eye.  The 
point  always  appears  at  the  place 

whence  these  rays  seem  to  emerge,  i.e.  at  the  real  apex  of 
the  cone.  If  the  direction  of  these  rays  be  changed  by  re- 
flection, or  in  any  other  manner,  the  point  will  appear  to  be 
in  the  direction  of  the  rays  as  they  enter  the  eye ;  thus  the 
point  A  appears  to  lie  in  the  direction  C  D ;  and  the  point  H, 
in  the  direction  C  N.  The  exact  location  of  these  points  may 
be  found  by  continuing  the  rays  CB  and  CE  behind  the 
mirror,  till  they  meet  at  the  points  D  and  N.  Thus,  the 
pencils  E  C  and  B  C  appear  to  emanate  from  the  points  N 
and  D ;  and  the  whole  body  of  light-waves  received  by  the 
eye  seems  to  come  from  an  jMmarent  object  ND  behind  the 

«/  -^*^4 _^ .— ««•>__ 

mirror.  This  apparent  object  is  called  an  image.  An  image 
is  a  point  or  a  series  of  points  from  which  a  diverging  pencil 
of  rays  comes  or  appears  to  come.  As  of  course  no  real 
image  can  be  formed  back  of  a  mirror,  such  an  image  is 
called  a  virtual  or  an  imaginary  image.  It  will  be  seen,  by 
construction,  that  an  image  in  a  plane  mirror  appears  as  far 


336  ETHER    DYNAMICS. 

behind  the  mirror  as  the  object  is  in  front  of  it,  and  is  of  the 
same  size  and  shape  as  the  object. 

It  appears  from  the  above  diagram  that  divergent  incident 
rays  remain  divergent  after  reflection  from  a  plane  mirror. 
In  a  like  manner  the  student  may  construct  diagrams,  and 
show  that  parallel  incident  rays  are  parallel  after  reflection, 
and  convergent  incident  rays  are  convergent  after  reflection, 
i.e.  reflection  from  a  plane  mirror  does  not  change  the  angle 
between  rays. 

297.  Reversion    of  images. — When   we   look   at  our   own 
faces  in  a  mirror  we  discover  a  lateral  reversion.     The  right 
cheek  is  the  left  cheek  in  the  image ;  the  hair  parted  on  the 
left  is  parted  on  the  right  in  the  image. 

If  the  mirror  be  vertical,  objects  appear  in  their  proper 
relations  to  the  horizon ;  but,  if  the  mirror  have  any  other 
position,  objects  assume  unnatural  postures.  Thus,  turn  this 
book  so  that  the  mirror  M  M  (Fig.  238)  may  represent  a  hori- 
zontal mirror,  and  AH  a  vertical  object  above  it,  and  it  will 
be  seen  that  the  image  appears  inverted.  To  verify  this, 
place  a  mirror  in  a  horizontal  position,  and  set  on  it  a  goblet 
of  water.  The  image  of  the  goblet  will  appear  upside  down. 
In  a  mirror  inclined  at  an  angle  of  45°  to  the  horizon,  the 
image  of  an  erect  object  appears  horizontal,  while  the  image 
of  a  horizontal  object  appears  erect. 

298.  Multiple  reflection ;  images  of  images. 

When  light  is  reflected  successively  from  two  plane  mirrors,  the 
image  in  the  first  becomes  the  object  for  the  second  mirror,  and 
the  second  image  is  found  in  precisely  the  same  manner  as  the  first 
one.  Again,  the  second  image  serves  as  an  object  for  a  third  image, 
and  so  on.  If  the  two  mirrors  be  parallel,  as  A  and  B  (Fig.  239), 
the  series  of  images,  theoretically  infinite  in  number,  is  formed  on 
a  common  straight  line  normal  to  the  mirrors  and  at  regularly  in- 
creasing distances  from  the  mirrors.  Thus  a'  is  the  primary  image 
of  the  object  a  in  mirror  A  (to  avoid  confusion,  a  pencil  from  only 
one  point  o  is  drawn).  The  light  reflected  at  c  enters  the  eye  as 


MULTIPLE    REFLECTION. 


337 


though  it  came  from  o'.  Other  rays  reflected  from  A  at  e  diverge 
as  though  they  emanated  from  a',  and  are  reflected  from  B  at  </, 
and  may  be  regarded  as  proceeding  from  a  real  object  at  a',  whose 
image  is  6,  as  far  back  of  B  as  of  is  in  front  of  B.  The  light  re- 
flected from  B  to  A  again  diverges  as  though  it  really  came  from  6, 
and  b  being  regarded  as  a  real  object,  its  image  would  be  formed 
at  a",  and  the  pencil  which  enters  the  eye  seems  to  proceed  from 


o'",  having  been  reflected  at  e"  as  though  it  came  from  o".  The 
pencil  which  would  enter  the  eye  from  a  third  image  at  the  left  of 
a"  may  be  traced  through  all  its  reflections  in  like  manner.  As 
some  light  is  lost  at  each  reflection,  the  images  decrease  in  bright- 
ness as  they  recede. 

A  kaleidoscope  is  constructed  on  the  principle  of  multiple  re- 
flection.    It  consists  of  a  tube  containing  three  mirrors  placed  at 
angles  of  60°.     Pieces  of  colored  glass,  free  to  move  at  one  end  of 
the  tube,  are  seen  through  an  eye-piece 
at  the  opposite  end  of  the  tube,  multi- 
plied by  repeated  reflections. 

Multiplied  images  of  a  small,  bright 
object,  as  of  a  candle  flame  (Fig.  240), 
often  seen  in  a  glass  mirror,  are  pro- 
duced by  repeated  reflections  between 
the  anterior  surface  and  the  silvered 
posterior  surface  of  the  mirror.  At 
each  internal  impact  on  the  first  sur- 
face some  light  escapes,  and  shows  us 
an  image,  while  another  portion  is  re- 
flected to  the  back,  and  thence  forward 
again,  showing  another  image,  and  so  on.  FIG.  240. 


338 


ETHER    DYNAMICS. 


FIG.  241. 


299.  Reflection  from  concave  mirrors.  —  Let  MM'  (Fig.  241) 
represent  a  section  of  a  concave  spherical  mirror,  which  may 
be  regarded  as  a  small  part  of  a  hollow  spherical  shell  having 

a  polished  interior 
surface.  The  distance 
MM'  is  called  the  di- 
ameter of  the  mirror. 
C  is  the  center  of  the 
sphere,  and  is  called 
the  center  of  curvature. 
G  is  the  vertex  of  the 
mirror.  A  straight  line  DG  drawn  through  the  center  of 
curvature  and  the  vertex  is  called  the  principal  axis  of  the 
mirror.  A  concave  mirror  may  be  considered  as  made  up  of 
an  infinite  number  of  small  plane  surfaces.  All  radii  of  the 
mirror,  as  CA,  CG,  and  CB,  are  perpendicular  to  the  small 
planes  which  they  strike.  If  C  be  a  luminous  point,  it  is 
evident  that  all  light-waves  emanating  from  this  point,  and 
striking  the  mirror,  will  be  reflected  to  their  source  at  C. 

Let  E  be  any  luminous  point  in  front  of  a  concave  mirror. 
To  find  the  direction  that  rays  emanating  from  this  point 
take  after  reflection,  draw  any  two  lines  from  this  point,  as 
EA  and  EB,  representing  two  of  the  infinite  number  of  rays 
composing  the  divergent  pencil  that  strikes  the  mirror.  Next, 
draw  radii  to  the  points  of  incidence  A  and  B,  and  draw  the 
lines  AF  and  BF,  making  the  angles  of  reflection  equal  to 
the  angles  of  incidence.  Place  arrow-heads  on  the  lines  rep- 
resenting rays  to  indicate  the  direction  of  the  motion.  The 
lines  AF  and  BF  represent  the  direction  of  the  rays  after 
reflection. 

It  will  be  seen  that  the  rays  after  reflection  are  convergent, 
and  meet  at  the  point  F,  called  the  focus.  This  point  is  the 
focus  of  all  reflected  rays  that  emanate  from  the  point  E.  It 
is  obvious  that  if  F  were  the  luminous  point,  the  lines  A  E 


REFLECTION    FROM    CONCAVE    MIRRORS.  339 

and  B  E  would  represent  the  reflected  rays,  and  E  would  be 
the  focus  of  these  rays.  Since  the  relation  between  the  two 
points  is  such  that  light-waves  emanating  from  either  one  are 
brought  by  reflection  to  a  focus  at  the  other,  these  points  are 
called  conjugate  foci.  Conjugate  foci  are  two  points  so  related 
that  the  image  of  either  is  formed  at  the  other.  The  rays  EA 
and  EB,  emanating  from  E,  are  less  divergent  than  rays  FA 
and  FB,  emanating  from  a  point  F  less  distant  from  the 
mirror,  and  striking  the  same  points.  Kays  emanating  from 
D,  and  striking  the  same  points  A  and  B,  will  be  still  less 
divergent ;  and  if  the  point  D  were  removed  to  a  distance  of 
many  miles,  the  rays  incident  at  these  points  would  be  very 
nearly  parallel.  Hence  rays  may  be  regarded  as  practically 
parallel  when  their  source  is  at  a  very  great  distance,  e.g.  the 
sun's  rays.  If  a  sunbeam,  consisting  of  a  bundle  of  parallel 
rays,  as  E  A,  D  G,  and  HB  (Fig.  242),  strike  a  concave  mirror 
in  a  direction  parallel  with  its  principal  axis,  M 

these  rays  become  convergent  by  reflection,        / 

and   meet   at    a  point   (F)  in  the  principal       /x>-^  p 
axis.     This  point,  called  the  principal  focus,      L/^-"""^  , 
is  about  half-way  between  the  center  of  curva-       \ 
ture  and  the  vertex  of  the  mirror.  M 

FlG.  242. 

On  the  other  hand,  it  is  obvious  that  di- 
vergent rays  emanating  from  the  principal  focus  of  a  concave 
mirror  become  parallel  by  reflection. 

If  a  small  piece  of  paper  be  placed  at  the  principal  focus 
of  a  concave  mirror,  and  the  mirror  be  exposed  to  the  parallel 
rays  of  the  sun,  the  paper  will  quickly  burn. 

Construct  a  diagram,  and  show  that  rays  proceeding  from  a 
point  between  the  principal  focus  and  the  mirror  are  divergent 
after  reflection,  but  less  divergent  than  the  incident  rays.  On 
reversing  the  direction  of  the  rays,  the  same  diagram  will 
show  that  convergent  rays  are  rendered  more  convergent  by 
reflection  from  concave  mirrors. 


340 


ETHER    DYNAMICS. 


The  general  effect  of  a  concave  mirror  is  to  increase  the  con- 
vergence or  to  decrease  the  divergence  of  incident  rays. 

300.  Spherical  aberration  of  mirrors. 

The  statement  that  parallel  rays  after  reflection  from  a  concave 
mirror  meet  at  the  principal  focus  is  only  approximately  true.  It 
is  strictly  true  only  of  parabolic  mirrors  such  as  are  used  in  the 
head-lights  of  locomotives.  Consequently  parabolic  mirrors  are 
used  when  it  is  desired  to  bring  the  plane-fronted  light-waves  of  a 
distant  star  accurately  to  a  focus,  or  to  change  a  divergent  pencil 
to  a  parallel  beam  ;  in  the  latter  case  the  source  of  light  is  placed  at 
the  focus  of  the  paraboloid.  In  spherical  mirrors  when  the  pencil 
is  broad,  the  outside  rays  or  those  which  are  incident  upon  the 
mirror  farthest  from  its  vertex  are  brought  to  a  focus  nearer  the 
mirror  than  the  inner  rays  ;  consequently  the  image  furnished  by 
a  luminous  point  is  a  circle  brightest  toward  its  center.  This  phe- 
nomenon is  called  the  spherical  aberration  of  a  mirror.  It  renders 
the  definition  of  the  images  of  objects,  especially  of  broad  objects, 

very  bad.  In  conse- 
quence of  this  it  is  often 
necessary  to  cut  off  the 
outside  rays  by  a  dia- 
phragm, which  improves 
the  definition  at  the  ex- 
pense of  the  brightness 
of  the  image. 

By  constructing  a 
number  of  rays  (Fig. 
243)  we  may  show  that 
all  rays  after  reflection 
are  tangent  to  a  charac- 
teristic curve  called  a 
caustic.  The  light  emit- 
ted from  a  single  point,  as  A,  is  spread  over  the  surface  produced 
by  the  revolution  of  the  line  ST  about  the  axis  AM.  This  curve 
formed  in  milk  by  reflection  from  the  interior  surface  of  a  bright 
tin  pail  is  commonly  called  "  the  cow's  foot." 

301.  Formation  of  images.  —  To   determine   the   position 
and  kind  of  images  formed  in  concave  mirrors  of  objects 


FIG.  243. 


FORMATION    OF    IMAGES. 


341 


FIG.  244. 


placed  in  front  of  them,  proceed  as  follows  :  Locate  the  ob- 
ject, as  DE  (Fig.  244).  Draw  lines,  EA  and  DB,  from  the 
extremities  of  the  object  through 
the  center  of  curvature  of  the  mir- 
ror, to  meet  the  mirror.  These  lines 
are  called  secondary  axes.  Incident 
rays  along  these  lines  will  return 
by  the  same  paths  after  reflection. 
Draw  another  line  from  D  to  any 
point  in  the  mirror,  e.g.  to  F,  to  rep- 
resent another  of  the  infinite  num- 
ber of  rays  emanating  from  D.  Make  the  angle  of  reflection 
CFD'  equal  to  the  angle  of  incidence  CFD,  and  the  reflected 
ray  will  intersect  the  secondary  axis  DB  at  the  point  D'. 
This  point  is  the  conjugate  focus  of  all  rays  proceeding  from 
D.  Consequently,  an  image  of  the  point  D  is  formed  at  D'. 
This  image  is  called  a  real  image,  because  rays  actually  meet 
at  this  point.  In  a  similar  manner,  find  the  point  E',  the 
conjugate  focus  of  the  point  E.  The  images  of  intermediate 

points  between  D  and  E  lie 
between  the  points  D'  and  E' ; 
and,  consequently,  the  image 
of  the  object  lies  between 
those  points  as  extremities. 

If,  for  the  second  ray  to  be 
drawn  from  any  point,  we 
select  that  ray  which  is  par- 
allel with  the  principal  axis, 
as  AGr  (Fig.  245),  it  will  not  be  necessary  to  measure  angles. 
For  this  ray,  after  reflection,  must  pass  through  the  principal 
focus  F ;  and  consequently  the  conjugate  focus  A'  is  easily 
found,  and  so  for  the  point  B'  and  intermediate  points.  Both 
methods  of  constructing  images  should  be  practiced  by  the 
pupil. 


FIG.  245. 


342 


ETHER    DYNAMICS. 


FIG.  246. 


It  thus  appears  that  an  image  of  an  object  placed  beyond  the 
center  of  curvature  of  a  concave  mirror  is  real,  inverted,  smaller 
than  the  object,  and  located  between  the  center  of  curvature  and 
the  principal  focus  of  the  mirror.  An  eye  placed  in  a  suitable 
position  to  receive  the  light,  as  at  H  (Fig.  246),  will  receive 

the  same  impression  from  the 
reflected  rays  as  if  the  image 
E'D'  were  a  real  object.  For 
a  cone  of  rays  originally  ema- 
nates from  (say)  the  point  D  of 
the  object,  but  it  enters  the 
eye  as  if  emanating  from  D', 
and  consequently  appears  to 
originate  from  the  latter  point.  A  person  standing  in  front 
of  such  a  mirror,  at  a  distance  greater  than  its  radius  of 
curvature,  will  see  an  image  of  himself  suspended,  as  it  were, 
in  mid-air.  Or,  if  in  a  darkened  room  an  illuminated  object 
be  placed  in  front  of  the  mirror,  and  a  small  oiled-paper  screen 
be  placed  where  the  image  is  formed,  a  large  audience  may 
see  the  image  projected  upon  the  screen. 

If  E'D'  (Fig.  246)  be  taken  as  the  object,  then  the  direc- 
tion of  the  light  in  the  diagram  will  be  reversed,  and  ED 
will  represent  the  image. 
Hence,  the  image  of  an 
object  placed  between  the 
principal  focus  and  the 
center  of  curvature  is  also 
real  and  inverted,  but 
larger  than  the  object,  and 
located  beyond  the  center 
of  curvature.  The  image  in  this  case  may  be  projected  upon 
a  screen,  but  it  will  not  be  so  bright  as  in  the  former  case, 
because  the  light  is  spread  over  a  larger  surface. 

Construct  an  image  of  an  object  placed  between  the  principal 


y^l"!! 


FIG.  247. 


FORMATION    OF    IMAGES. 


343 


M 


FIG.  248. 


focus  and  the  mirror,  as   in  Fig.  247.      It  will  be  seen  in 

this  case  that  a  pencil  of  rays  proceeding  from  any  point  of 

an  object,  e.g.  P,  has  no  actual  focus,  but 

appears  to  proceed  from  a  virtual  focus 

])',  back  of  the  mirror,  and  so  with  other 

points,   as    E.      The  image  of  an   object 

placed   between    the  principal  focus    and 

the   mirror    is    virtual,   erect,   larger  than 

the  object,  and  back  of  the  mirror. 

The  diagram  in  Fig.  248  suggests  the 
method  of  finding  the  disposition  of  a  pencil  of  rays  emanating 
from  any  point  (e.g.  A)  after  reflection  from  a  convex  mirror. 
Construct  an  image  of  an  object  placed  in  front  of  a  convex 
mirror. 

302.    Illustrative  experiments. 

Experiment  3.  — Hold  some  object,  e.g.  a  rose,  as  ab  (Fig.  249),  a  few 
feet  in  front  of  a  concave  mirror.     Looking  in  the  direction  of  the  axis 

of  the  mirror  you  see  a 
small  inverted  image, 
AB,  of  the  object,  be- 
tween the  center  of  cur- 
vature, C,  of  the  mirror 
and  its  principal  focus, 


F. 

Evidently  if  AB  rep- 
resent an  object  placed 
between  the  principal 
focus  and  the  center  of 
curvature;  then  ab  will 
represent  the  image  of 
the  object. 

Experiment  4. — Place  a  candle  in  an  otherwise  dark  room  20  feet 
from  the  mirror,  catch  the  focused  light-waves  upon  a  paper  screen,  and 
show  that  the  focus  is  about  half-way  between  the  vertex  and  the  center 
of  curvature  of  the  mirror. 

Experiment  5.  —  Advance  the  distant  candle  flame  toward  the  mirror, 
moving  it  up  and  down.  (1)  Show  that  the  focus  advances  to  meet  the 


FIG.  249. 


344  ETHER    DYNAMICS. 

flame,  and  that  when  the  flame  is  raised  the  focus  is  depressed,  and  the 
converse.  (2)  Show  that  when  the  flame  is  at  the  center  of  curvature, 
the  focus  is  also  there.  (3)  Show  that  when  the  flame  is  between  the 
center  of  curvature  and  the  principal  focus,  the  focus  of  the  flame  is 
farther  away  than  the  center  of  curvature.  (4)  Show  that  when  the 
flame  is  at  the  principal  focus,  the  reflected  rays  are  parallel,  or  the  focus 
is  at  an  infinite  distance.  (5)  Show  that  when  the  flame  is  still  nearer, 
the  reflected  rays  diverge  and  appear  to  come  from  a  point  behind  the 
mirror.  (6)  Notice  that  in  all  cases  except  the  last  the  images  are  real 
and  inverted,  and  that  in  all  cases  where  a  real  image  is  formed,  the 
flame  and  the  image  may  change  places. 

Experiment  6.  —  Form  a  real  image  of  the  flame  between  yourself  and 
the  mirror;  view  the  image  through  a  convex  lens  (§  318);  show  that 
the  image  can  be  magnified  by  a  convex  lens,  and  thereby  illustrate  the 
principle  of  the  astronomical  reflecting  telescope  (§  388). 

When  light  emitted  by  a  luminous  point  at  a  distance  /  is  reflected  by 
a  concave  spherical  mirror,  it  is  reflected  back  to  an  approximate  focus 
at  a  distance  /'.  The  relation  between  the  distance  of  the  source  /,  the 
distance  of  the  focus  /',  and  the  radius  of  the  mirror  r,  is  expressed  by 
the  following  simple  formula  l : 

(1)    -f  +  J>  =  -r' 
From  this  equation  we  get 


which  gives  the  distance  of  the  image  from  the  mirror  in  terms  of  /  and  r. 

2 

(a)  Since  the  sum  of  the  reciprocals  of  /  and  /'  is  a  constant,     ,  it  fol- 
lows that  as/  increases/'  decreases,  and  when/  becomes  infinite/'  =  -• 

Hence  parallel  rays  (Le.  rays  from  an  infinitely  distant  source)  come  to  a 
focus  at  a  point  half  way  between  a  mirror  and  its  center  of  curvature. 

When/  =  -,  /'=  oo  .  i.e.  rays  emanating  from  the  principal  focus  become 

parallel,  and  the  waves  plane-fronted. 

(&)  When  /  decreases  /'  increases,  i.e.  the  object  and  image  approach 

2      2 
each  other.     When  /  equals  /',  -  =  -,  i.e.  object  and  image  coincide  at 

the  center  of  curvature. 

1  See  Ganot,  p.  434  ;  Barker,  p.  416. 


FORMATION    OF    IMAGES.  345 

r     1  2 

(c)  When  /  is  less  than  - ,  -  is  greater  than  - ,  and  /'  is  therefore 

negative,  and  the  image  is  behind  the  mirror,  and  hence  virtual.  Dis- 
tances in  front  of  the  mirror  are  considered  positive,  and  those  back  of 
the  mirror  negative. 

(Questions. 

1.  When  an  object  is  located  at  a  distance  from  a  concave  mirror 
equal  to  its  radius,  will  any  image  be  formed  ?     Why  ? 

2.  What  is  the  effect  of  placing  the  object  at  the  principal  focus? 
Why? 

o.  a.  When  is  the  real  image  formed  by  a  concave  mirror  smaller 
than  the  object  ?  6.  When  is  it  larger  ? 

4.  a.  When  is  the  image  formed  by  a  concave  mirror  real  ?     6.  When 
is  it  virtual  ? 

5.  a.  Is  the  image  of  an  object  formed  by  a  convex  mirror  real  or 
virtual  ?     b.  Is  it  larger  or  smaller  than  the  object  ?     c.    Is  it  erect  or 
inverted  ? 

6.  Is  the  general  effect  of  a  convex  mirror  to  collect  or  to  scatter  rays  ? 
7. .  The  radius  of  a  concave  spherical  mirror  is  20  inches.     Determine 

the  conjugate  focus  for  a  point  on  the  principal  axis  15  inches  from  the 
mirror. 

8.    Why  do  images  formed  by  a  surface  of  water  appear  inverted  ? 

0.  a.  What  kind  of  wave-front  has  a  beam  of  parallel  rays  ?  b.  What 
change  in  front  of  such  a. beam  occurs  when  it  strikes  each  of  the  follow- 
ing mirrors  :  viz.  a  plane,  a  concave,  and  a  convex  mirror  ? 

10.  Where  is  the  conjugate  focus  of  light  emanating  from  each  of  the 
following  points  :   a.    the   center  of  curvature   of  a  concave   spherical 
mirror  :  b.  a  point  on  the  principal  axis  at  an  infinite  distance  from  the 
mirror  ;  c.  a  point  on  the  principal  axis  beyond  the  center  of  curvature 
and  at  a  finite  distance  from  the  mirror  ;  d.  a  point  on  the  principal  axis 
between  the  center  of  curvature  and  the  principal  focus  ;  e.  a  point  be- 
tween the  principal  focus  and  the  vertex  ? 

11.  How  could  you  find  the  radius  of  curvature  of  a  concave  spherical 
mirror  by  optical  means  alone  ? 


346 


ETHER   DYNAMICS. 


SECTION  VI. 


B 


REFRACTION. 

303.    Introductory  experiments. 

Experiment  1.  —  Into  a  darkened  room  admit  a  sunbeam  so  that  its 
rays  may  fall  obliquely  on  the  bottom  of  the  basin  (Fig.  250),  and  note 
the  place  on  the  bottom  where  the  edge  of  the  shadow  DE  cast  by  the 

side  of  the  basin  D  C  meets  the  bottom 
G  at  E.  Then,  without  moving  the  basin, 
fill  it  evenly  full  with  water  slightly 
clouded  with  milk  or  with  a  few  drops 
of  a  solution  of  mastic  in  alcohol.  It 
will  be  found  that  the  edge  of  the  shadow 
has  moved  from  D  E  to  D  F,  and  meets 
the  bottom  at  F.  Beat  a  blackboard 
rubber,  and  create  a  cloud  of  dust  in 
the  path  of  the  beam  in  the  air,  and  you 
will  discover  that  the  rays  GD  that 
graze  the  edge  of  the  basin  at  D  become 
bent  at  the  point  where  they  enter  the 

water,  and  now  move  in  the  bent  line  GDF,  instead  of,  as  formerly,  in 
the  straight  line  G  D  E.  The  path  of  the  line  in  the  water  is  now  nearer 
to  the  vertical  side  D  C ;  in  other  words,  this  part  of  the  beam  is  more 
nearly  vertical  than  before. 

Experiment  2.  —  Place  a  coin  (A,  Fig.  251)  on  the  bottom  of  an  empty 
basin,  so  that,  as  you  look  through  a  small  hole  in  a  card  BC  over  the 
edge  of  the  vessel,  the  coin  is  just  out  of  sight. 
Then,  without  moving  the  card  or  basin,  fill  the 
latter  with  water.  Now,  on  looking  through 
the  aperture  in  the  card,  the  coin  is  visible. 
The  beam  AE,  which  formerly  moved  in  the 
straight  line  AD,  is  now  bent  at  E,  where  it 
leaves  the  water,  and,  passing  through  the  aper- 
ture in  the  card,  enters  the  eye.  Observe  that 
as  the  beam  passes  from  the  water  into  the  air  it 
is  turned  farther  from  a  vertical  line  E  F ;  in  other  words,  the  beam  is 
farther  from  the  vertical  than  before. 


FIG.  251. 


CAUSE    OF    REFRACTION.  347 

Experiment  3.  —  From  the  same  position  as  in  the  last  experiment, 
direct  the  eye  to  the  point  G  in  the  basin  filled  with  water.  Reach  your 
hand  around  the  basin,  and  place  your  finger  where  that  point  appears 
to  be.  On  examination,  it  will  be  found  that  your  finger  is  considerably 
above  the  bottom.  Hence,  the  effect  of  the  bending  of  rays,  as  they  pass 
obliquely  out  of  water,  is  to  cause  the  bottom  to  appear  more  elevated  than 
it  really  is;  in  other  words,  to  cause  the  water  to  appear  shallower  than 
it  is. 

Experiment  4-  —  Thrust  a  pencil  obliquely  into  water ;  it  will  appear 
shortened,  and  bent  at  the  surface  of  the  water,  and  the  immersed  portion 
will  appear  elevated. 

Experiment  5.  —  Place  a  piece  of  wire  (Fig.  252)  vertically 
in  front  of  the  eye,  and  hold  a  narrow  strip  of  thick  plate  glass 
horizontally  across  the  wire,  so  that  the  light-waves  from  the 
wire  may  pass  obliquely  through  the  glass  to  the  eye.     The  wire 
will  appear  to  be  broken  at  the  two  edges  of  the  glass,  and  the          ' 
intervening  section  will  appear  to  the  right  or  left  according 
to  the.  inclination  of  the  glass ;  but  if  the  glass  be  not  inclined  to  the  one 
side  or  the  other,  the  wire  does  not  appear  broken. 

When  a  ray  of  light  passes  from  one  medium  into  another 
of  different  density,  it  is  bent  or  refracted  at  the  interface 
between  the  two  mediums  unless  it  meet  this  plane  perpen- 
dicularly. In  the  latter  case  there  is  no  refraction.  If  it 
pass  into  an  optically  denser  medium,  it  is  refracted  toward 
the  perpendicular  to  this  plane  ;  if  into  a  rarer  medium,  it  is 
refracted  from  the  perpendicular.  It  is  not  universally  true 
that  the  denser  mediums  are  the  more  highly  refracting. 
The  refractive  power  of  water  is  less  than  that  of  alcohol  or 
oil  of  turpentine.  A  substance  which  has  a  higher  refractive 
power  than  another  is  said  to  be  optically  denser. 

The  angle  GDO  (Fig.  250)  is  called  the  angle  of  incidence; 
FDN,  the  angle  of  refraction;  and  EDF,  the- angle  of  devia- 
tion. 

304.  Cause  of  refraction.  —  Foucault  and  others  have 
proved  by  careful  experiments  that  the  speed  of  light  is 
much  less  in  water  than  in  air.  It  is  less  in  glass  than  in 


348 


ETHER   DYNAMICS. 


water,  and  much  less  in  diamond  than  in  glass.  Every  trans- 
parent substance  has  its  own  rate  of  transmission.  It  would 
seem  that  there  is  an  interaction  between  the  ether  and  the 
molecules  of  matter  such  that  in  different  mediums  the  ether- 
waves  are  unequally  retarded. 

Let  the  series  of  parallel  lines  AB  (Fig.  253)  represent  a 

series  of  wave-fronts  leaving  an 
object  C,  and  passing  through  a 
rectangular  piece  of  glass  DE, 
and  constituting  a  beam.  Every 
point  in  a  wave-front  moves  with 
equal  velocity  as  long  as  it  trav- 
erses the  same  medium ;  but  the 
point  a  of  a  given  wave  ab  enters 
the  glass  first,  and  its  velocity  is 
impeded,  while  the  point  I  re- 
tains its  original  velocity;  so 
that,  while  the  point  a  moves  to 
a',  b  moves  to  b'}  and  the  result  is  that  the  wave-front  assumes 
a  new  direction  (very  much  in  the  same  manner  as  a  line  of 
soldiers  executes  a  wheel),  and  a  ray  or  a  line  drawn  perpen- 
dicularly through  the  series  of  waves  is  turned  out  of  its 
original  direction  on  entering  the  glass.  Again,  the  extremity 
c  of  a  given  wave-front  cd  first  emerges  from  the  glass,  when 
its  velocity  is  immediately  quickened  ;  so  that,  while  d  ad- 
vances to  d',  c  advances  to  c',  and  the  direction  of  the  ray  is 
again  changed.  The  direction  of  the  ray  after  emerging 
from  the  glass  is  parallel  to  its  direction  before  entering  it, 
but  it  has  suffered  a  lateral  displacement. 

It  is  evident  that  if  the  ray  enter  the  new  medium  in  a 
direction  perpendicular  to  its  surface,  i.e.  with  its  wave- 
front  parallel  to  this  surface,  all  parts  of  the  wave-front 
will  be  retarded  simultaneously  and  no  refraction  will  take 
place. 


FlG.  253 


THE    WAVE-THEORY    APPLIED    TO    REFRACTION.       349 


305.    The  wave-theory  applied  to  refraction. 

Let  K  A,  ND,  etc.  (Fig.  254),  be  parallel  rays  of  a  beam  of  light 
falling  on  a  plane  refracting  surface  AD.  Let  KLMN  denote  the 
plane  front  of  a  wave.  The  wave  reaches  the  refracting  surface 
first  at  A,  and  then 
successively  at  other 
points  in  A  B  C  D. 
As  soon  as  the  wave 
reaches  A,  that  point 
becomes  the  origin 
of  an  undulation 
in  the  ether  which 
spreads  out  in  all 
directions  in  the  me- 
dium in  the  form  of 
a  sphere  having  its 
center  at  A.  The 
"speed  with  which 
motion  is  propagated 
in  the  new  medium  we  suppose  to  be  less  than  that  in  the  first 
medium.  Describe  a  circle  with  the  center  A,  and  with  a  radius 
equal  to  the  distance  a  wave  would  move  in  the  new  medium  in  the 
same  time  as  it  would  describe  the  excess  of  N  D  over  K  A  in  the 
first  medium.  Let  circles  be  described  from  B,  C,  and  other  points 
of  AD,  according  to  the  same  law.  Then  a  straight  line  abcD 
touching  all  these  circles  represents  a  plane  refracted  wave.  It  can 
be  demonstrated  that  the  sine  (see  §  307)  of  the  angle  K  A  G  bears 
the  same  ratio  to  the  sine  of  the  angle  aAH  as  the  speed  of  light 
in  the  first  medium  bears  to  the  speed  in  the  new  medium,  i.e.  as 
the  excess  of  N  D  over  K  A  bears  to  A  a. 


FIG.  254. 


306.    Failure  of  the  emission  theory  to  account  for  the  refrac- 
tion of  light. 

To  explain  refraction  from  a  rare  to  a  denser  medium  according 
to  the  emission  theory  of  light  it  is  necessary  to  assume  that  when 
a  light  particle  shot  from  a  luminous  body  comes  within  a  very 
small  distance  of  the  surface  of  separation  between  two  mediums, 
it  begins  to  be  attracted  towards  the  surface  so  that  its  component 


350 


ETHER    DYNAMICS. 


velocity  perpendicular  to  the  surface  gradually  increases  till  it 
reaches  a  limited  distance  on  the  other  side  of  the  surface.  That  is, 
the  speed  of  light  should  be  by  the  theory  greater  in  dense  than  in 
rarer  mediums  ;  whereas  the  reverse  is  found  to  be  true.  Hence 
the  failure  of  the  emission  theory  to  account  for  the  phenomenon 
of  refraction. 

307.  Index  of  refraction.  —  The  deviation  of  light-waves  in 
passing  from  one  medium  into  another,  depends  upon  the 
mediums  and  the  angle  of  incidence.  It  diminishes  as  the 
angle  of  incidence  diminishes,  and  is  zero  when  the  incident 
ray  is  normal.  It  is  highly  important,  knowing  the  angle  of 
incidence,  to  be  able  to  determine  the  direction  which  a  ray 

will  take  on  entering  a  new 
medium.  Describe  a  circle 
around  the  point  of  inci- 
dence A  (Fig.  255)  as  a 
center ;  through  the  same 
point  draw  IH  perpendicu- 
lar to  the  surfaces  of  the 
two  mediums,  and  to  this 
line  drop  perpendiculars 
B  D  and  C  E  from  the  points 
where  the  circle  cuts  the 
ray  in  the  two  mediums. 
Then  suppose  that  the  per- 
pendicular BD  is  T%  of  the  radius  AB  ;  now  this  fraction 
T8ff  is  called  (in  trigonometry)  the  sine  of  the  angle  DAB. 
Hence,  T^_  is  the  sine  of  the  angle  of  incidence.  Again,  if  we 
suppose  that  the  perpendicular  CE  is  T%  of  the  radius,  then 
the  fraction  T%  is  the  sine  of  the  angle  of  refraction.  The 
sines  of  the  two  angles  are  to  each  other  as  T%  :  T6^,  or  as 
4:3.  The  quotient  (in  this  case  4=1.33+)  obtained  by 
dividing  the  sine  of  the  angle  of  incidence  by  the  sine  of 
the  angle  of  refraction,  generally  expressed  in  the  form  of  a 


SNELL'S  "LAW  LAW  OF  SINES."  351 

decimal  fraction,  is  called  the  index  of  refraction.  It  can  be 
proved  to  be  the  ratio  of  the  velocity  of  the  incident  to  that  of 
the  refracted  light-waves. 

308.  Snell's  "Law  of  Sines."  -  -We  have  found  that  a  ray 
of  light  in  passing  obliquely  from  a  medium  into  another  of 
different  density  suffers  refraction,  and  the  greater  the  angle 
of  incidence  the  greater  the  deflection.    *Snell  in  1621  dis- 
covered the  law  which  governs  these  variable  angles  of  de- 
flection.    It  is  called  the  "law  of  sines":  "The  incident  and 
refracted  rays  are  in  the  same  plane  with  the  normal  to  the 
surface;  they  lie  on  opposite  sides  of  it,  and  the  sines  of  their 
inclinations  bear  a  constant  ratio  to  each  other"     The  incident 
ray  may  be  more  or  less  oblique,  still  the  index  of  refraction 
remains  the  same. 

309.  Indices  of  refraction.  —  The  index  of  refraction  for 
light-waves  in  passing  from  air  into  water  is  approximately  f , 
and  from  air  into  glass  f ;  of  course,  if  the  order  be  reversed, 
the  reciprocal  of  these  fractions  must  be  taken  as  the  indices  ; 
e.g.  from  water  into  air,  the  index  is  f ;  from  glass  into  air,  |. 
When  a  ray  passes  from  a  vacuum  into  a  medium,  the  re- 
fractive index  is  greater  than  unity,  and  is  called  the  absolute 
index  of  refraction.      The  relative  index  of  refraction,  from  any 
medium  A  into  another  B,  is  found  by  dividing  the  absolute 
index  of  B  by  the  absolute  index  of  A. 

It  will  be  shown  later  that  the  refractive  index  varies  with 
wave-length.  The  following  table  is  intended  to  represent 
mean  indices  for  light-waves  :  — 

TABLE  or  ABSOLUTE  INDICES. 


Lead  chromate 2.07 

Diamond  (about) 2.5 

Carbon  disulphide  .     .     .     .     .     1.64 
Flint  glass  (about)  .....     1.61 

Agate 1.54 

Canada  balsam   .  ,1.53 


Crown  glass  (about)      .     .     .  1.53 

Spirits  of  turpentine     .     .     .  1.48 

Alcohol 1.37 

Humors  of  the  eye  (about)    .  1.35 

Pure  water 1.33 

Air  at  0°  C.  and  760™"  pressure  1.000294 


352 


ETHER   DYNAMICS. 


310.  Given  the  direction    of  the   incident  ray  and   the  re- 
fractive index.,  to  determine  the  direction  of  the  refracted  ray.  — 
Let  L  0  (Fig.  256)  be  the  incident  ray ;  draw  a  circle  with 

the  point  of  incidence,  0,  as  a  center. 
Divide  0  C  by  the  refractive  index,  and 
set  off  the  quotient,  O  D,  on  the  other 
side  of  0.  Draw  DB  perpendicular  to 
the  surface  at  D,  meeting  the  circum- 
ference at  B;  then  0  B  is  the  direction 
of  the  refracted  ray  required.  For  it  is 

0  C 
FIG.  256.  apparent  that    -— -  is  the   same    as  the 

ratio  of  the  sines,  and  this  ratio  is  by  construction  equal  to 
the  refractive  index. 

311.  Some   phenomena    of   refraction.      Refraction   into    a 
rarer  medium.  —  A  stick  partly  immersed  in  water  appears 
to   be   bent   upwards    and   shortened  unless   its   position  is 
vertical,  when  the  part 

immersed  appears  sim- 
ply shortened.  Fig. 
257  explains  this.  The 
dotted  lines  represent 
the  real  position  of  the 
submerged  part  of  the 
stick,  and  dotted  lines 
diverging  from  a  point 
at  the  bottom  of  the 
stick  show  the  course 
of  the  rays  which  reach 
the  eye  from  that  point.  On  reaching  the  surface  they  are 
bent  from  the  perpendicular,  and  the  bottom  of  the  stick  is 
seen  in  the  direction  from  which  the  rays  actually  enter  the  eye. 
Viewed  obliquely,  the  depth  of  water  cannot  appear  greater 
than  |  its  real  depth.  Hence  the  shoaling  effect  of  still 


FIG.  257. 


CRITICAL    ANGLE. 


353 


water  in  which  the  bottom  is  visible.  To  an  eye  under 
water  the  surface  must  appear  at  least  |  of  its  real  dis- 
tance. 

312.     Critical  angle;  total  reflection.  —  Let  S  S'  (Fig.  258) 
represent  the  boundary  surface  between  two  mediums,  and 
A  0  and  B  0  incident  rays  in  the  more   refractive   medium 
(e.g.  glass);  then  0  D  and  OE  may  represent  the  same  rays 
respectively  after  they  enter  the  less  refractive  medium  (e.g. 
air).       It    will    be 
seen    that,    as    the 
angle    of    incidence 
is  increased,  the  re- 
fracted ray  rapidly 
approaches  the  sur- 
face    0  S.        Now,    I 
there    must    be    an    | 
angle   of    incidence    ! 
(e.g.  COM)  such  that    f  \^ 
the  angle  of  refrac-    \        cx  /X^ 
tion  will  be  90°;  in    |  ^feJ 

this    case   the  inci- 
dent ray  CO,  after 

refraction,  will  just  graze  the  surface  0  S.  This  angle  (COM) 
is  called  the  critical  or  limiting  angle.  Any  incident  ray,  mak- 
ing a  larger  angle  with  the  normal  than  the  critical  angle,  as 
L  0,  cannot  emerge  from  the  medium,  and  consequently  is 
not  refracted.  Experiment  shows  that  all  such  rays  undergo 
internal  reflection  ;  e.g.  the  ray  L  0  is  reflected  in  the  direc- 
tion ON.  Reflection  in  this  case  is  perfect,  and  hence  is 
called  total  reflection.  Total  reflection  occurs  when  rays  in  the 
more  refractive  medium  are  incident  at  an  angle  greater  than 
the  critical  angle. 

Surfaces    of    transparent    mediums,    under   these   circum- 
stances, constitute   the  best  mirrors  possible.     The  critical 


354 


ETHER    DYNAMICS. 


angle  diminishes  as  the  refractive  index 1  increases.  For 
water  it  is  about  48£°  ;  for  flint  glass,  38°  41';  and  for  the 
diamond,  23°  41'.  Light- waves  cannot,  therefore,  pass  out  of 
water  into  air  with  a  greater  angle  of  incidence  than  48^-°. 
The  brilliancy  of  gems,  particularly  the  diamond,  is  due  in 
part  to  their  extraordinary  power  of  reflection,  arising  from 
their  large  indices  of  refraction. 

313.    Illustrations  of  refraction  and  total  reflection. 

Experiment  6.  —  Observe  the  image  of  a  candle  flame  reflected  by  the 
surface  of  water  in  a  glass  beaker,  as  in  Fig.  251). 

Experiment  7.  —  Thrust  the  closed  end  of  a  glass  test-tube  (Fig.  260) 
into  water,  and  incline  the  tube.  Look  down  upon  the  immersed  part 


FIG.  259. 


FIG.  260. 


of  the  tube,  and  its  upper  surface  will  look  like  burnished  silver,  or  as  if 
the  tube  contained  mercury.  Fill  the  test-tube  with  water,  and  immerse 
as  before  ;  the  total  reflection  which  before  occurred  at  the  surface  of  the 
air  in  the  submerged  tube  now  disappears.  Explain. 

1  It  must  be  evident  on  inspection  of  Fig.  258  that  a  ray  traveling  in  the  direc- 
tion SO  will  be  refracted  in  the  direction  OC.  The  angle  SOK  is  a  right  angle, 
and  the  sine  of  a  right  angle  =  1.  Therefore  the  index  of  refraction  of  the  medium 

=  —  Thus,  to  get  the  index  of  refraction  of  any  substance  it  is  only 

sin  cnt.  ang. 

necessary  to  find  the  critical  angle  of  the  substance.  This  principle  has  been  applied 
by  Kohlrausch  in  his  total  reflectometer,  in  determining  indices  of  refraction  of 
crystals. 


A    LUMINOUS    CASCADE. 


355 


B 


FIG.  261. 


A  glass  prism  of  90°  is  often  used  as  a  reflector.     Light 

passes  through  the  surface   AB  (Fig.   261)  and  meets  the 

surface  A  C  at  an  angle  of  45°,  which  is  r 

greater  than  the  critical  angle  for  glass. 

It  is  therefore  totally  reflected,  and  the 

device  is  consequently  more    effective        , 

than  an  ordinary  mirror. 

314.    A  luminous  cascade.  —  If  water 

be  siphoned  through  a  glass  tube  having 

an  open  side  tubule,  a  (Fig.  262),  and 

the  tube   below  a  be  exposed  to  the 

direct  rays  of  the  sun  or  placed  in  the  path  of  a  beam  of 

light  from  a  lantern  or  porte-lumiere,  the  stream  of  water 
mingled  with  air  which  enters  the 
tubule  will  appear  like  a  "  stream 
of  living  fire,"  and  has  received  the 
name  of  luminous  cascade.  This  is 
due  to  total  reflection.  The  light  in 
passing  through  the  water  meets  the 
surface  of  the  air-bubbles  at  angles 
greater  than  the  critical,  and  is 
reflected  from  side  to  side  all  down 
the  stream. 


FIG.  262. 


Experiment  8.  —  Place  uncolored  glass  beads,  or  glass  broken  into  small 
pieces  in  a  test-tube.  They  appear  not  only  white,  because  of  diffused 
reflection,  but  quite  opaque,  because  of  refraction  and  internal  reflection. 
Pour  some  water  into  the  tube,  and  it  becomes  somewhat  translucent. 
Substitute  spirits  of  turpentine  for  the  water,  and  the  translucency  is 
increased. 

By  mixing  a  small  quantity  of  carbon  bisulphide  with  the  turpentine, 
or  olive  oil  with  oil  of  cassia,  a  liquid  can  be  obtained  whose  refractive 
index  is  about  the  same  as  that  of  glass,  when  the  light  will  pass  through 
the  liquid  without  obstruction,  and  the  beads  become  transparent  and 
nearly  invisible.  The  last  illustration  shows  that  one  transparent  body 
within  another  can  be  seen  only  when  their  refractive  indices  differ.  Place 


356 


ETHER    DYNAMICS. 


H 


FIG. 


your  eye  on  a  level  with  the  surface  of  a  hot  stove,  and  you  may  observe 
a  wavy  motion  in  the  air,  due  to  the  mingling  of  currents  of  heated  and 

less  refractive   air  with  cooler  and 
more  refractive  air. 

A  ray  of  light  from  a  heavenly 
body  A  (Fig.  263)  undergoes  a  series 
of  refractions  as  it  reaches  successive 
strata  of  the  atmosphere  of  constantly 
increasing  density,  and  to  an  eye  at 
the  earth's  surface  appears  to  come 
from  a  point  A'  in  the  heavens.  The 
general  effect  of  the  atmosphere  on 
the  path  of  light  that  traverses  it  is 
such  as  to  increase  the  apparent 
altitude  of  the  heavenly  bodies.  It 
enables  us  to  see  a  body  (B)  which 
is  actually  below  the  horizon,  and 

prolongs  the  apparent  stay  of  the  sun,  moon,  and  other  heavenly  bodies, 
above  the  horizon.1  Twilight  is  due  both  to  refraction  and  reflection  of 
light  by  the  atmosphere. 

Exercises. 

1.  Draw  a  straight  line  to  represent  a  surface  of  flint  glass,  and  draw 
another  line  meeting  this  obliquely  to  represent  a  ray  of  light  passing 
from  a  vacuum  into  this  medium.     Find  the  direction  of  the  ray  after  it 
enters  the  medium,  employing  the  index  as  given  in  the  above  table. 

2.  a.  Determine  the  relative  index  of  refraction  for  light  in  passing 
from  water  into  diamond.     b.  In  passing  from  water  into  air. 

3.  How  must  one  modify  his  aim  in  shooting  or  spearing  fish  from  the 
bank  of  a  stream  ? 

4.  A  ray  is  incident  on  a  surface  of  crown  glass  at  an  angle  of  40° ; 
find  the  angle  of  refraction. 

5.  Find  the  refractive  index  for  light  passing  from  water  into  crown 
glass. 

6.  Does  a  star  in  the  zenith  appear  to  be  where  it  really  is  ?     Why  ? 


1  Under  average  conditions  the  refraction  elevates  a  body  at  the  horizon  about  35', 
so  that  both  the  sun  and  the  moon  in  rising  appear  clear  of  the  horizon  while  still 
wholly  below  it.  The  amount  of  refraction  varies  sensibly  with  the  temperature  and 
barometric  pressure,  increasing  as  the  thermometer  falls  or  as  the  barometer  rises. 


OPTICAL    PRISMS. 


357 


SECTION  VII. 

PRISMS    AND    LENSES. 

315.  Optical  prisms.  —  An  optical  prism  is  a  portion  of  a 
transparent  medium  bounded  by  plane  surfaces  inclined  to 
each  other.  Fig.  264  represents  a  transverse  section  of  a 
common  form  of  prism.  Let 
AB  be  a  ray  of  light  incident 
upon  one  of  its  surfaces.  On 
entering  the  prism  it  is  re- 
fracted toward  the  normal,  and 
takes  the  direction  EC.  On 
emerging  from  the  prism  it  is 
again  refracted,  but  now  from 
the  normal  in  the  direction  C  D. 
will  appear  to  be  at  F. 


FIG 


The  object  that  emits  the  ray 
Observe  that  the  ray  A  B,  at  both  refrac- 
tions, is  bent  toward  the  thicker  part,  or  base,  of  the  prism, 
316.    Measuring  index  of  refraction. 

The  ray  S  (Fig.  265)  strikes  the  face  A  C  of  a  prism  at  the  angle 
of  incidence  i,  and  is  refracted  at  the  angle  r ;  sin  i  =  n  sin  r,  (1),  n 
being  the  index  of  refraction.  It  strikes  the  face  A  B  at  the  angle 

r',  and  leaves  the  prism 

A  at  the  angle  i'  \  sin  i' = 

n  sin    r'  (2).      It    may 
be  proved  geometrically 
that  the  angles  r  and  r' 
are  together  equal  to  the 
angle  of  the  prism  A  ; 
r+r'=  A  (3).     Also,  if 
the  angle  between    the 
incident    ray    SD    pro- 
duced and  the  deviated  ray  E  S'  be  V  (i.e.  the  angle  GO  S',  called  the 
angle  of  deviation)  then  i  +  i'  =  V+  A  (4).  From  these  four  equations, 
which  involve  n,  together  with  any  three  of  the  six  angles,  i,  i',  r, 
r',  A,   V,  we  may  determine  for  any  given  monochromatic    light 
(§  357)  the  index  of  refraction  n  of  the  material  of  the  prism. 


FIG.  265. 


358 


ETHER    DYNAMICS, 


317.  Minimum  deviation. 

Furthermore,  it  can  be  shown  that  when  the  prism  is  so  placed 
that  i'  becomes  equal  to  i,  the  angle  of  deviation,  V,  of  the  ray  has 
its  least  value.  Such  a  position  is  shown  in  Fig.  264,  and  is  called 
the  position  of  minimum  deviation.  It  is  easily  obtained  in  practice 
by  turning  the  prism  until  a  certain  position  is  obtained  where  the 
beam  of  light,  S',  comes  to  a  standstill  and  begins  to  move  back,  no 
matter  which  way  the  prism  is  rotated. 

318.  Lenses.  —  Any  transparent  medium  bounded  by  sur- 
faces of  which  at  least  one  is  curved,  is  a  lens. 

Lenses  are  of  two  classes,  converging  and  diverging,  ac- 
cording as  they  collect  rays  or  cause  them  to  diverge.  Each 
class  comprises  three  kinds  (Fig.  266) :  — 

CLASS  I.  CLASS  II. 


1.  Bi-convex1 

2.  Plano-convex 

3.  Concavo-convex 

(or  meniscus) 


Converging,  or 
convex  lenses, 
thicker  in  the 
middle  than  at 
the  edges. 


4.  Bi-concave        }  Diverging,  or  con- 

5.  Plano-concave  I      ca ve  lenses,  thin- 

6.  Convexo-con-    j      ner  in  the  middle 

cave  J     than  at  the  edges. 


A  straight  line  normal  to  both  surfaces  of  a  lens  and  pass- 
ing through  their  centers    of    curvature,    as  A  B,  is  called 

its  principal  axis. 
There  is  a  point  in 
B_  the  principal  axis 
of  every  lens  called 
its    optical    center. 
FIG-  266<  This    point    is    so 

placed  that  a  ray  whose  direction  within  the  lens  passes 
through  it  suffers  no  angular  deviation,  but  at  most  only  a 
slight  lateral  displacement.  In  lenses  1  and  4  it  is  half-way 
between  their  respective  curved  surfaces.2  A  ray  drawn 

1  If  the  two  convex  surfaces  be  of  different  curvature,  the    lens    is  called   a 
"  crossed  lens." 

2  In  lens  2  the  optical  center  is  in  its  convex  surface  ;  in  lens  5  it  is  in  its  concave 
surface  ;  in  lenses  3  and  6  it  is  without  the  lens. 


EFFECT  OF  LENSES. 


359 


through  the  optical  center  from  any  point  of  an  object,  as  Aa 
(Fig.  274),  is  called  the  secondary  axis  of  this  point. 

319.  Effect  of  lenses.  —  We  may,  for  convenience  of  illus- 
tration, regard  a  biconvex  lens  as  composed,  approximately, 
of  a  series  of  prisms  of  gradually  increasing  angles  arranged 
around  an  axis,  as  represented  in  section  in  Fig.  267.  It 
is  apparent  that  the  parallel  rays 
farthest  from  the  principal  axis,  /j\ 

meeting     prisms     of    greater     and  ,'j\ 

greater  angles  of  incidence,  are 
more  deflected  than  those  nearer  the 
axis  ;  and  if  the  curvatures  be 
properly  adjusted,  all  may  be  made 
to  converge  to  one  point. 

On  the  other  hand  if  the  lens  be 
thinnest  at  the  center  and  gradually 
increase  in  thickness  outward,  exact- 
ly the  opposite  effect  would  be  ex- 
pected. Parallel  incident  rays,  being 
bent  toward  the  thicker  part  of  the 
component  prisms,  would  become 
separated. 

The  general  effect  of  all  convex  lenses  is  to  cause  transmitted 
rays  to  converge  ;  that  of  concave  lenses,  to  cause  them  to  diverge. 
Incident  rays  parallel  to  the  principal  axis  of  a  convex  lens 

are  brought  to  a  focus  F 
(Fig.  268)  at  a  point  in  the 
principal  axis.  This  point 
is  called  the  principal  focus, 
i.e.  it  is  the  focus  of  incident 
rays  parallel  to  the  principal 
axis.  It  may  be  found  by  holding  the  lens  so  that  the  rays 
of  the  sun  may  fall  perpendicularly  upon  it,  and  then  moving 
a  sheet  of  paper  back  and  forth  behind  it  until  the  image  of 


FIG.  267. 


FIG.  268. 


360 


ETHER    DYNAMICS. 


I 


FIG.  269. 


the  sun  formed  on  the  paper  is  brightest  and  smallest.  Or, 
in  a  room,  it  may  be  found  approximately  by  holding  a  lens 
at  a  considerable  distance  from  a  window,  and  regulating  the 
distance  so  that  a  distinct  image  of  the  window  will  be  pro- 

jected  upon 
the  opposite 
wall,  as  in 
Fig.  269.  The 
focal  length  is 
the  distance 
from  the  opti- 
cal center  of 
the  lens  to  the 
center  of  the 
image  on  the 
paper.  The 

shorter  the  focal  length  the  more  powerful  is  the  lens  ; 
that  is,  the  more  quickly  are  the  parallel  rays  that  traverse 
different  parts  of  the  lens  brought  to  cross  one  another. 

If  the  paper  be  kept  at  the  principal  focus  for  a  short  time, 
it  will  take  fire.  The  reason  is  apparent  why  convex  lenses  are 
sometimes  called 
"burning  glasses." 
A  pencil  of  rays, 
emitted  from  the 
principal  focus  F 
(Fig.  268)  as  a 
luminous  point,  be- 
comes parallel  on 
emerging  from  a  convex  lens.  If  the  rays  emanate  from  a 
point^  nearer  the  lens,  they  diverge  after  egress,  but  the 
divergence  is  less  than  before  ;  if  from  a  point  beyond  the 
principal  focus,  the  rays  are  rendered  convergent.  A  concave 
lens  causes  parallel  incident  rays  to  diverge  as  if  they  came 


FIG.  270. 


CONJUGATE    FOCI.  361 

from  a  point,  as  F  (Fig.  270).     This   point  is  therefore  its 
principal  focus.     It  is,  of  course,  a  virtual  focus. 

Every  lens  has  a  principal  focus ;  it  is  the  point  to  which 
parallel  rays  are  caused  to  converge,  or  from  which,  after 
deflection,  they  appear  to  diverge,  as  the  case  may  be. 

320.  Conjugate  foci.  —  When  a  luminous  point  beyond  the 
principal  focus,  S  (Fig.  271),  sends  rays  to  a  convex  lens,  the 
emergent    rays 

converge  to  an- 
other point  S';    sVr^!:r^  .~^H^^^^^^^  S' 
rays  sent  from 
S'   to   the   lens 
would  converge                                     FlG-  271< 
to  S.     Two  points  thus  related  are  called  conjugate  foci.     The 
fact  that  rays  which  emanate  from  one  point  are  caused  by 
convex  lenses  to  collect  at  one  point,  gives  rise  to  real  images, 
as  in  the  case  of  concave  mirrors. 

321.  Law  of  converging  lenses. 

Lenses,  like  mirrors,  have  conjugate  foci  at  distances  p  and  p' 
from  the  optical  centers.  In  converging  lenses  the  principal  focal 
distance  and  the  distance  of  their  conjugate  foci  (or  distance  of  ob- 
ject and  image)  are  related  according  to  the  formula 

1  +  1  _  1 . 
P      P'      f 

Hence  the  law  of  converging  lenses :  The  reciprocal  of  the  princi- 
pal focal  length  is  equal  to  the  sum  of  the  reciprocals  of  any  two  con- 
jugate focal  lengths. 

When  a  pencil  of  light  comes  from  an  infinite  distance  (i.e.  when 
its  rays  are  parallel),  p  =  <x>  ;  then  p'  =/,  and  the  rays  converge  at 
the  principal  focus.  Conversely,  if  a  pencil  come,  from  the  principal 
focus,  p  =/;  hence  p'  =  oo  ;  that  is,  no  image  is  formed. 

If  the  object  (i.e.  the  source  of  light)  be  at  a  distance  less  than 
infinity,  but  greater  than  2/,  the  image  is  real,  and  is  on  the  other 
side  of  the  lens  at  a  distance  greater  than/ and  less  than  2f.  Con- 
versely, if  the  object  be  at  a  distance  greater  than  /,  but  less  than 
2/,  the  image  is  at  a  distance  greater  than  2/. 


362  ETHER   DYNAMICS. 

If  the  object  be  at  a  distance  2/,  the  image  is  also  at  the  distance 
2/,  and  object  and  image  are  of  equal  size.  This  suggests  a  simple 
way  of  finding  /.  Adjust  an  object,  convex  lens,  and  screen,  so 
that  the  image  on  the  screen  is  equal  in  size  to  the  object.  Half 
the  distance  of  either  the  object  or  its  image  from  the  center  of  the 
lens  is  the  focal  length  of  the  lens. 

322.  Diverging  lenses. 

The  formula  for  these  is ,  =  -  • 

P      P      f 

When  p  =  oo  ,  p'  =  —  f  (a  virtual  image  at  the  principal  focus  *). 
When  p  =  /,  p'  =  —  co  (no  image). 

When  p  is  of  any  value  greater  than  /,  and  less  than  cc  ,  p'  is 
greater  than  /. 

323.  Images  formed.  —  Fairly  distinct  images  of  objects 
may   be  formed  through  very   small   apertures  (§  283);  but 
owing  to  the  small  amount  of  light  that  passes  through  the 
aperture,  the  images  are  very  deficient  in  brilliancy.     If  the 
aperture  be  enlarged,  brilliancy  is  increased  at  the  expense  of 
distinctness.      A  convex  lens  enables  us  to  obtain  both  brilliancy 
and  distinctness  at  the  same  time. 

Experiment  1.  — By  means  of  a  porte-lumiere,  A  (Fig.  272),  introduce 
a  horizontal  beam  of  light  into  a  darkened  room.  In  its  path  place  some 
object,  as  B,  painted  in  transparent  colors  or  photographed  on  glass. 
(Transparent  pictures  are  cheaply  prepared  by  photographers  for  sunlight 
and  lime-light  projections.)  Beyond  the  object  place  a  convex  lens  L, 
and  beyond  the  lens  a  screen  S.  The  object  being  illuminated  by  the 
beam  of  light,  all  the  rays  diverging  from  any  point  a  are  bent  by  the 
lens  so  as  to  come  together  at  the  point  a'.  In  like  manner,  all  the  rays 
proceeding  from  c  are  brought  to  the  same  point  c' ;  and  so  also  for  all 
intermediate  points.  Thus,  out  of  the  billions  of  rays  emanating  from 
each  of  the  millions  of  points  on  the  object,  those  that  reach  the  lens  are 
guided  by  it,  each  to  its  own  appropriate  point  in  the  image.  It  is 
evident  that  there  must  result  an  image  both  bright  and  distinct,  pro- 
vided the  screen  be  suitably  placed,  i.e.  at  the  place  where  the  rays  meet. 

i  The  negative  sign  refers  to  the  direction  in  which  p'  is  measured.  Conjugate 
foci  of  diverging  lenses  are  on  the  same  side  of  the  lens. 


IMAGES    FORMED. 


363 


But  if  the  screen  be  placed  at  S'  or  S",  it  is  evident  that  a  blurred  image 
will  be  formed.  Instead  of  moving  the  screen  back  and  forth,  in  order 
to  "focus "  the  rays  properly,  it  is  customary  to  move  the  lens.  • 

Experiment  2.  —  Make  a  series  of  experiments  similar  to  those  with 
the  concave  mirror.     Ascertain  the  focal  length  of  the  convex  lens. 


FIG.  272. 


Place  the  lens  at  a  distance  from  a  white  wall  about  equal  to  its  focal 
length.  Place  a  candle  flame  (better  the  flame  of  a  fish-tail  burner)  at 
such  a  distance  the  other  side  of  the  lens  that  it  will  produce  a  distinct 
and  well-defined  image  on  the  wall  (Fig.  273).  (1)  Observe  and  note  on 


FIG.  273. 


paper  the  size  and  kind  of  image.  Advance  the  flame  toward  the  lens, 
regulating  at  the  same  time  the  distance  between  the  lens  and  wall,  so  as 
to  preserve  a  distinctness  of  image.  (2)  Note  the  changes  which  the 


364 


ETHER    DYNAMICS. 


image  undergoes.  (3)  When  the  image  and  the  flame  become  of  the 
same  size,  measure  and  note  the  distance  of  each  from  the  lens.  (4)  Ad- 
vance the  flame  still  nearer,  and  note  the  changes  in  the  image,  until  it  is 
impossible  to  obtain  an  image  on  the  wall.  Measure  the  distance  of  the 
flame  from  the  lens,  and  compare  this  distance  with  the  focal  length  of 
the  lens.  (5)  Move  the  flame  still  nearer.  Note  whether  the  rays,  after 
emerging  from  the  lens,  are  divergent  or  convergent.  (6)  See  whether  an 
image  and  an  object  may  change  places.  (7)  Form  images  of  the  flame 
on  the  wall  at  different  distances  from  the  lens ;  measure  the  distances, 
also  the  linear  dimensions  (e.g.  the  width,  or  the  vertical  hight)  of  the 
images,  and  determine  whether  the  linear  dimensions  of  images  are  pro- 
portional to  their  distances  from  the  lens. 

324.  To  construct  the  image  formed  by  a  convex  lens.  — 
Given  .the  lens  L  (Fig.  274),  whose  principal  focus  is  at  F, 
and  object  A  B  in  front  of  it ;  any  two  of  the  many  rays  from 

6 


Fm.  274. 


A  will  determine  where  its  image  a  is  formed.  Two  that  can 
be  traced  easily  are,  one  along  the  secondary  axis  A  0  a,  and 
one  parallel  to  the  principal  axis  A  A':  the  latter  will  be 
deviated  so  as  to  pass  through  the  principal  focus  F,  and 
will  afterward  intersect  the  secondary  axis  at  some  point  a ; 
therefore  this  is  the  conjugate  focus  of  A.  Kays  can  be 
similarly  traced  for  B,  and  all  intermediate  points  along  the 
arrow.  Thus,  a  real  inverted  image  is  formed  at  a  b. 

The  linear  dimensions  of  an  object  and  of  its  image  formed 
by  a  convex,  lens  are  proportional  to  their  respective  distances 
from  the  center  of  the  lens.  The  image  is  virtual  or  real,  erect 
or  inverted,  according  as  it  is  on  the  same  side  of  the  lens 
with  the  object  or  on  the  opposite  side. 


VIRTUAL    IMAGES. 


365 


325.  Virtual   images.  —  Since   rays   that  emanate  from  a 
point  nearer  the  lens  than  the  principal  focus  diverge  after 
egress,  it  is  evident  that  their  focus  must  be  virtual  and  on 
the  same  side  of  the  lens  as  the  object.     Hence,  the  image  of 
an  object  placed  nearer  the  lens  than  the  principal  focus  is 
virtual,  magnified,  and  erect,  as  shown  in  Fig.  275.     A  convex 
lens  used  in  this  manner  is  called  a  simple  microscope. 

326.  Simple  microscope.     As  its  name  implies,  the  micro- 
scope   is   an   instrument  for  viewing   minute    objects.     The 
simple  microscope   consists  of   a  single  converging  lens   so 
placed  that  the  object  is  between  the  principal  focus  and  the 
lens.     It  magnifies  by  increasing  the  visual  angle. 

A' 


B' 


FIG.  275. 


The  magnifying  poiver  of  the  lens  is  simply  the  ratio 
between  the  apparent  diameter  of  the  image  and  the  diameter 
of  the  object,  e.g.  A'B':  AB  (Fig.  275),  or  it  is  the  ratio 
between  the  visual  angles  under  which  the  eye  would  see 
image  and  object,  if  both  were  placed  at  the  distance,  of 
distinct  vision.1  If  the  lens  be  of  short  focus,  as  is  usually 
the  case,  the  magnifying  power  is  approximately  the  ratio  of 
the  distance  of  distinct  vision  to  the  focal  length.  Thus  a 
lens  of  -J  in.  focal  length  would  magnify  20  to  24  diameters. 


1  For  normal  eyes,  an  object  to  be  seen  most  distinctly  must  be  placed  at  a 
distance  of  10  to  12  inches,  hence  this  is  regarded  as  the  distance  of  distinct  vision. 


366 


ETHER    DYNAMICS. 


327.  Diverging  lenses.  —  Since  the  effect  of  concave  lenses 
is  to  render  transmitted  rays  divergent,  pencils  of  rays 
emitted  from  A  and  B  (Fig.  276)  diverge  after  refraction,  as 
if  they  came  from  A'  and  B',  and  the  image  will  appear  to  be 
at  A'  B'.  Hence,  images  formed  by  concave  lenses  are  virtual, 
erect,  and  smaller  than  the  object. 


FIG.  276. 


328.  Spherical  aberration.  —  In  all  ordinary  convex  lenses 
the  curved  surfaces  are  spherical,  and  the  angles  which  inci- 
dent rays  make  with  the  little  plane  surfaces  of  which  we 
may  imagine  the  spherical  surface  to  be  made  up,  increase 


FIG.  277. 

rapidly  toward  the  edge  of  the  lens.  Thus,  while  those  rays 
from  a  given  point  of  an  object  which  pass  through  the  cen- 
tral portion,  as  A  (Fig.  277),  meet  approximately  at  the  same 
point  F,  those  which  pass  through  the  marginal  portion  are 
deflected  so  much  that  they  cross  the  axis  at  nearer  points, 
e.g.  at  F' ;  so  a  blurred  image  results.  This  wandering  of  the 
rays  from  a  single  focus  is  called  spherical  aberration. 

No  lens  with  spherical  surfaces  can  bring  all  the  rays  to 
the  same  focus.     The  evil  may  be  in  a  measure  corrected  by 


SPHERICAL   ABERRATION.  367 

interposing  a  diaphragm  D  D'  provided  with  a  central  aperture 
smaller  than  the  lens,  so  as  to  cut  off  those  rays  that  pass 
through  the  marginal  part  of  the  lens.  But  it  can  be  wholly 
corrected  only  by  properly  modifying  the  curvature  of  the 
surfaces  of  the  lens.  A  lens  having  surfaces  thus  modified  is 
said  to  be  aplanatic. 

Experiment  3.  —  (Illustrating  spherical  aberration.)  Cut  a  cardboard 
disk  as  large  as  the  convex  lens  to  be  employed.  Cut  a  ring  of  holes 
near  the  circumference,  and  also  a  ring  near  the  center.  Support  the 
disk  close  to  the  lens,  so  as  to  cover  one  of  its  surfaces.  Place  the  whole 
in  a  beam  from  a  porte-lumiere.  Catch  refracted  beams  on  a  screen. 
.Move  the  screen  away  from  the  lens.  The  beams  through  the  outer  ring 
of  spots  are  the  first  to  cross  one  another  and  form  an  image.  Further 
away,  the  inner  beams  coincide,  forming  an  image.  The  outer  ones, 
having  crossed,  form  a  ring  of  spots. 

Questions. 

1.  What  must  be  the  position  of  an  object  with  reference  to  aeon- 
verging  lens,  that  its  image  may  be  real  and  magnified  ? 

2.  A  photographic  transparency  is  placed  between  a  porte-lumiere  and 
a  biconvex  lens,  16  in.  from  the  latter  ;  how  many  diameters  is  a  distinct 
image  of  the  transparency  multiplied-  on  a  screen  20  ft.  distant  ? 

3.  A  transparency  whose  dimensions  are  3  X  4  in.  is  placed  1 6  in.  from 
the  lens  ;  at  what  distance  from  the  lens  must  the  screen  be  that  it  may 
receive  a  distinct  image  of  the  transparency  that  shall  cover  a  surface 
3  X  4  ft.  ? 

4.  What  is  the  focal  length  of  the  lens  used  in  the  last  case  ? 

5.  With  a  converging  lens  the  image  of  a  candle  is  thrown  on  a  screen 
6  ft.  from  the  candle,  and  the  focal  length  of  the  lens  is  16  in.  ;  find  the 
distances  of  the  candle  and  of  the  screen  from  the  lens.    -4ns.  4  ft.  and  2  ft. 

6.  A  luminous  point  is  3  in.  from  a  convex  lens  having  a  focal  length 
of  5  in.  ;  find  the  position  of  the  image. 

7.  If  the  candle  and  screen  be  3  ft.  apart,  and  the  lens  midway  between 
them,  what  is  the  focal  length  ? 

8.  Find  the  focal  length  of  a  lens  which  throws  the  image  of  an  object 
5  ft.  distant  on  a  screen  3  ft.  distant. 

9.  A  double  concave  lens  having  a  focal  length  of  3  in.  is  held  at  a 
distance  of  2  in.  from  a  small  object ;  find  the  position  of  the  image. 


368 


ETHER    DYNAMICS. 


10.  If  an  object  be  at  twice  the  focal  distance  of  a  convex  lens,  how 
will  the  length  of  the  image  compare  with  the  length  of  the  object  ? 

11.  To  an  eye  whose  distance  of  distinct  vision  is  25  cm,  how  many 
diameters  will  a  lens  of  1  cm  focus  magnify  ? 

12.  Show  that  a  concave  air  lens  in  water  has  the  same  effect  on  inci- 
dent light  as  a  convex  water  lens  in  air. 


SECTION  VIII. 


PRISMATIC    ANALYSIS    OF    LIGHT.  -  SPECTRUMS. 

329.    Analysis  of  light  which  produces  the  sensation  of  white. 

Experiment  1.  —  Place  a  disk  with  an  adjustable  slit  in  the  aperture  of 
a  porte-lumiere,  so  as  to  exclude  from  a  darkened  room  all  light-waves 
except  those  which  pass  through  the  slit.  Near  the  slit  interpose  a 


FIG.  278. 


double-convex  lens  of  (say)  10-inch  focus.  A  narrow  sheet  of  light  will 
traverse  the  room  and  produce  an  image,  AB  (Fig.  278),  of  the  slit  on  a 
white  screen  placed  in  its  path.  Now  place  a  glass  prism  C  in  the  path 
of  the  narrow  sheet  of  light  and  near  to  the  lens,  with  its  edge  vertical. 


ANALYSIS    OF    LIGHT.  369 

(1)  The  light  now  is  not  only  turned  from  its  former  path,  but  that  which 
before  was  a  narrow  sheet,  is,  after  emerging  from  the  prism,  spread  out 
fan-like  into  a  wedge-shaped  body,  with  its  thickest  part  resting  on  the 
screen.     (2)  The  image,  before  only  a  narrow,  vertical  band,  A  B,  is  now 
drawn  out  into  a  long  horizontal  ribbon  DE.      (3)  The  image,  before 
white,  now  presents  all  the  colors  of  the  rainbow,  from  red  at  one  end 
to  violet  at  the  other ;  it  passes  gradually  through  all  the  gradations  of 
orange,  yellow,  green,  blue,  and  violet.      (The  difference  in  deviation 
between  the  red  and  the  violet  is  purposely  much  exaggerated  in  the 
figure. ) 

From  this  experiment  we  learn  (!)•  that  white  light  is  not 
simple  in  its  composition,  but  the  result  of  a  mixture  of  colors.1 

(2)  The  colors  of  which  white  light  is  composed  may  be  sepa- 
rated by  refraction.     (3)  The  separation  is  due  to  the  different 
degrees  of  deviation  which  colors  undergo  by  refraction.     Red, 
which  is  always  least  turned  aside  from  a  straight  path,  is 
the   least    refrangible    color.      Then   follow  orange,  yellow, 
green,  blue,  and  violet,  in  the  order  of  their  refrangibility. 
The  many-colored  ribbon  of  light  DE  is  called  the  solar  spec- 
trum?    This  separation  of  white  light  into  its  constituents  is 
called  dispersion.     The  number  of  colors  of  which  white  light 
is  composed  is  really  infinite,  but  we  have  names  for  only 
seven  of  them  ;  viz.  red,  orange,  yelloiv,  green,  cyan-blue,  ultra- 
marine-blue, and  violet ;  and  these  are  called  the  primary  or 
prismatic  colors.     The  names  of  the  blues  are  derived  from 
the  names  of  the  pigments  which  most  closely  resemble  them. 

The  spectrum  may  be  projected  upon  a  screen,  or  it  may  be 
received  directly  by  the  eye,  as  in  the  two  following  experi- 
ments :  — 

Experiment  2.  —  Upon  a  black  cardboard  A  (Fig.  279)  paste  a  strip 
of  white  paper  3  cm  long  and  2  mm  wide  ;  and  place  the  prism  and  the 
eye  as  in  the  figure.  Now  when  a  beam  of  white  light  from  the  strip  is 

1  Newton  (1666)  was  the  first  to  recognize  the  true  import  of  this  phenomenon,  i.e. 
to  refer  the  colors  to  the  heterogeneity  of  white  light. 

2A  succession  of  colors  in  the  order  of  their  refrangibility,  obtained  from  any 
source  of  light,  is  called  a  spectrum. 


370 


ETHER    DYNAMICS. 


refracted  and  dispersed  by  the  prism  and  falls  upon  the  retina  of  the  eye, 
you  see,  not  the  narrow  white  strip  in  its  true  position,  but  a  spectrum 
in  the  position  A'.  This  experiment  is  performed  in  a  lighted  room. 

A'  Experiment  3.  — Instead  of  a  continuous  white 

strip,  paste  short  strips  of  red,  white,  and  blue, 
end  to  end,  on  the  black  card,  as  represented  in 
Fig.  280.  The  spectrum  of  each  color  is  given  on 
the  right,  the  light  portions  representing  the  illu- 
minated parts.  It  will  be  seen 
that  in  the  spectrum  of  the  red, 
the  green,  blue,  and  violet 
portions  are  almost  completely 
dark,  but  there  is  a  faint  trace 
of  orange  ;  in  the  spectrum  of 
the  blue,  the  red,  orange,  and 
yellow  are  wanting,  blue  and 
violet  are  present,  and  a  small 
FIG.  279.  quantity  of  green.  FJG 

330.  Synthesis  of  white  light.  —  The  composition  of  white 
light  has  been  ascertained  by  the  process  of  analysis  ;  it  can 
be  verified  by  synthesis ;  i.e.  the  colors  after  dispersion  may 
be  reunited,  and  the  result  of  the  reunion  is  white  light. 

Experiment  4.  —  Place  a  second  prism  (2)  in  such  a  position  £57  that 
light  which  has  passed  through  one  prism  (1),  and  been  refracted  and 
decomposed,  may  be  refracted  back,  and  the  colors  will  be  reblended, 
and  a  white  image  of  the  slit  will  be  restored  on  the  screen. 

Experiment  5. — Place  a  large  convex  lens,  or  a  concave  mirror 
(better  a  concave  cylindrical  mirror),  so  as  to  receive  the  colors  after  dis- 
persion by  a  prism,  and  bring  the  rays  to  a  focus  on  a  screen.  The 
image  produced  will  be  white. 

Experiment  6. — Receive  the  spectrum  on  a  common  plane  mirror, 
and  rapidly  tip  the  mirror  back  and  forth  in  small  arcs,  and  the  light 
reflected  by  the  mirror  upon  a  screen  will  produce  a  white  image  on  the 
screen. 

331.  The  rainbow.  —  The  rainbow  is  a  solar  spectrum  on  a 
grand  scale.     It  is  the  result  of  refraction,  total  reflection, 


CHROMATIC    ABERRATION. 


371 


and  dispersion,  of  sunlight  by  falling  raindrops.  Let  spheres 
1  and  2  (Fig.  281)  represent  drops  at  the  extreme  opposite 
edges  of  the  bow.  The  eye  is  in  a  position  to  receive,  after 
the  dispersion  and  internal  reflection  of  the  light-waves  within 
drop  1,  only  the  red  waves ;  consequently  this  part  of  the 
bow  appears  red.  So,  likewise,  from  drop  2  the  eye  receives 
only  violet ;  consequently  this  part  of  the  bow  appears  violet. 
In  like  manner,  the  intermediate  colors  of  the  bow  are 
sifted  out. 

Outside  the  primary  bow  a  secondary  bow  is  sometimes  seen. 
Drops  3  and  4  (Fig.  281)  are  supposed  to  be  at  the  opposite 


FIG.  281. 


edges  of  the  secondary  bow.  It  will  be  seen  that  the  light- 
waves undergo  two  internal  reflections  within  the  drops 
which  produce  this  bow.  The  colors  of  this  bow  are  in 
reverse  order  to  those  of  the  primary  bow,  and  less  brilliant. 
332.  Chromatic  aberration.  —  There  is  also  in  ordinary 
convex  lenses  a  serious  defect,  to  which  we  have  not  before 
referred,  called  chromatic  aberration,  the  correction  of  which 
has  demanded  the  highest  skill.  The  convex  lens  both  refracts 


372  ETHER    DYNAMICS. 

and  disperses  the  light-waves  that  pass  through  it.  The  ten- 
dency, of  course,  is  to  bring  to  a  focus  the  more  refrangible 
rays,  as  the  violet,  much  sooner  than  the  less  refrangible 
rays,  such  as  the  red.  The  result  is  a  disagreeable  coloration 
of  the  images  that  are  formed  by  the  lens,  especially  by  those 
portions  of  the  light-waves  that  pass  through  the  lens  near 
its  edges.  This  evil  has  been  overcome  very 
effectually  by  combining  with  the  convex  lens 
a  plano-concave  lens.  Now,  if  a  crown-glass 
convex  lens  be  taken,  a  flint-glass  concave 
lens  may  be  prepared  that  will  correct  the  dispersion  of  the 
former  without  neutralizing  all  its  refraction.1  A  compound 
lens  composed  of  these  two  lenses  cemented  together  (Fig.  282) 
constitutes  what  is  called  an  achromatic  lens. 

333.  Cause  of  color  and  dispersion.  —  The  color  of  light  is 
determined  by  vibration-frequency,  or,  in  other  words,  by  the 
corresponding  wave-length.  The  light-waves  diminish  in 
length  from  the  red  to  the  violet.  As  pitch  depends  on 
the  frequency  with  which  aerial  waves  strike  the  ear,  so  color 
depends  upon  the  frequency  with  which  ether-waves  strike 
the  eye.  The  difference  between  violet  and  red  is  a  difference 
analogous  to  the  difference  between  a  high  note  and  a  low 
note  on  a  piano. 

The  speed  of  propagation  in  a  vacuum  appears  to  be  the 
same  for  all  wave-lengths.  But  in  a  refracting  medium,  the 
short  waves  are  more  retarded  than  the  longer  ones,  hence 
they  are  more  refracted.  This  is  the  cause  of  dispersion. 
Each  wave-length  has  its  own  refractive  index,  or,  since 
vibration-frequency  corresponds  to  color,  every  simple  color 
has  its  special  refractive  index.  Light  composed  of  waves  all 
of  the  same  (or  nearly  the  same)  length  is  called  homogeneous 
or  monochromatic  light.  The  yellow  light  emitted  by  the 
flame  of  a  Bunsen  burner  or  alcohol  lamp  when  common  salt 

1  The  refractive  and  dispersive  powers  of  the  two  lenses  are  not  proportional. 


CAUSE    OF    COLOR    AND    DISPERSION.  373 

is  sifted  upon  it  is  approximately  monochromatic.     Ordinary 
white  light  is  a  mixture  of  long  and  short  ether-waves. 

From  well-established  data,  determined  by  a  variety  of 
methods,  physicists  have  calculated  the  number  of  waves  that 
succeed  one  another  for  each  of  the  several  prismatic  colors, 
and  the  corresponding  wave-lengths  ;  the  following  table  con: 
tains  the  results.1  The  letters  A,  C,  D,  etc.  refer  to  Fraun- 
hofer's  lines  (see  §  340). 

Length  of  waves  No.  of  waves 

in  millimeters.  per  second. 

Dark  red A .000760 395, 000,000,000,000 

Orange C 000656  ... 458,000,000,000,000 

Yellow D 000589 510,000,000,000,000 

Green E .000527 570,000,000,000,000 

C.  Blue F .000480 618,000,000,000,000 

U.  Blue G .000431 697,000,000,000,000 

Violet H    .  .000397 760,000,000,000,000 

There  is  a  limit  to  the  sensibility  of  the  eye  as  well  as  of 
the  ear.  The  limit  in  the  number  of  vibrations  appreciable 
by  the  eye  lies  approximately  within  the  range  of  numbers 
given  in  the  above  table  ;  i.e.  if  the  succession  of  waves  be 
muqji  more  or  much  less  rapid  than  is  indicated  by  these 
numbers,  the  sensation  of  sight  is  not  produced. 

"  Our  knowledge  of  ether-waves  is  at  present  limited  to 
those  which  lie  between  107  trillions  and  40,000  trillions  per 
second  —  a  range,  in  musical  parlance,  of  about  8|-  octaves" 
(Langley).  Of  these  our  eyes  are  sensitive  to  scarcely  one 
octave. 

It  is  evident  that  the  frequency  of  the  waves  emitted  by  a 
luminous  body,  and  consequently  the  color  of  the  light  emitted, 

1  "  That  man  should  be  able  to  measure,  with  certainty,  such  minute  portions  of 
space  and  time,  is  not  a  little  wonderful ;  for,  whatever  theory  of  light  we  adopt,  it 
may  be  observed  that  these  periods  and  these  spaces  have  a  real  existence,  being,  in 
fact,  deduced  by  Newton  himself  from  direct  measurements,  and  involving  nothing 
hypothetical  but  the  names  here  given  them."  —  Sir  John  Herschel. 

If  science  in  the  future  shall  be  able  to  dispense  with  the  ether  of  space,  the 
vibration  periods  and  what  corresponds  to  wave-lengths  will  necessarily  remain. 


374  ETHER    DYNAMICS. 

must  depend  on  the  rapidity  of  the  vibratory  motions  of  the 
molecules  of  that  body,  i.e.  upon  its  temperature.  This  has 
been  shown  in  a  convincing  manner  as  follows  :  The  temper- 
ature of  a  platinum  wire  is  slowly  raised  by  passing  a 
gradually  increasing  current  of  electricity  through  it.  At  a 
temperature  of  about  540°  C.  it  begins  to  emit  light ;  and  if 
the  light  be  analyzed  by  a  prism,  it  is  shown  that  only  red 
light  is  emitted.  As  the  temperature  rises,  there  will  be 
added  to  the  red  of  the  spectrum,  first  yellow,  then  green, 
blue,  and  violet  successively.  When  it  reaches  a  white  heat, 
it  emits  all  the  prismatic  colors.  It  is  significant  that  a 
white-hot  body  emits  more  red  light  than  a  red-hot  body,  and 
likewise  more  light  of  every  color  than  at  any  lower  temper- 
ature. The  conclusion  is,  that  a  body  which  emits  white  Uyht 
sends  forth  simultaneously  waves  of  a  variety  of  lengths. 

334.  Continuous  spectrums.  —  The   spectrum  produced  by 
the  platinum  is  continuous  ;    that  is,  the  band  of  light  is 
unbroken.     If  the  spectrum  be  not  complete,   as  when  the 
temperature  is  too  low,  it  will  begin  with  red,  and  be  con- 
tinuous as  far  as  it  goes.     All  luminous  solids  and  liquids  give 
continuous  spectrums.  • 

A  gas,  kerosene,  or  candle  flame  does  not  give  the  spectrum 
of  a  vapor,  but  gives  that  of  the  solid  particles  of  carbon  in  a 
state  of  incandescence  ;  hence  the  continuous  spectrums  which 
these  flames  afford. 

335.  Spectroscopes.  —  Instruments   for  the  observation   of 
spectrums  are  called  spectroscopes.     The  essential  part  of  the 
apparatus  is  the  "dispersion  piece,"  which  is  either  a  prism 
or  a  diffraction  grating  (see  Fig.  302).     Instead  of  looking  at 
the  spectrum  with  the  naked  eye  it  is  usually  better  to  view 
it   through  a  small  telescope,  which  serves  to  magnify  it. 
Fig.  283  represents  the  simplest  form  of  the  Kirchhoff  and 
Bunsen   spectroscope.     A   flint   glass    prism    receives    light 
through  an  adjustable   slit  at  the  end  of  a  tube  called  the 


SPECTROSCOPES. 


375 


collimator.  At  the  opposite  end  of  this  tube  is  a  converging 
lens,  and  the  slit  is  located  at  its  principal  focus  so  that  rays 
diverging  from  the  slit  are  rendered  parallel  by  the  lens. 

It  is  often  necessary  to  have  some  means  of  determining 
the  positions  of   certain   lines   (to   be   described   hereafter) 


FIG.  283. 


observed  in  the  spectrum.  The  usual  method  is  to  have  a 
second  tube,  somewhat  like  the  collimating  tube,  so  placed  . 
that  the  rays  from  a  light  (e.g.  a  candle  flame  as  in  Fig. 
283)  after  passing  through  a  transparent  plate  (inside  the 
tube)  on  which  a  fine  scale  is  engraved,  and  through  a  lens, 
by  which  they  are  made  parallel,  are  reflected  from  the 


376  ETHER    DYNAMICS. 

nearest  face  of  the  prism,  and  pass  into  the  telescope  along 
with  the  beam  of  light  under  analysis.  Thus  the  eye  while 
viewing  the  spectrum  through  the  telescope  sees  also  a 
magnified  image  of  the  scale  coinciding  with  the  spectrum. 

336.  Direct -vision  pocket  spectroscope.  —  A  small  instru- 
ment called  a  pocket  spectroscope  will  answer  fairly  well  for 
experiments  given  in  this  book.  This  instrument  contains 
three  or  more  prisms,  A,  B,  and  C  (Fig.  284).  The  prisms 
are  enclosed  in  a  brass  tube,  D,  and  this  tube  in  another  tube, 
E.  F  is  a  convex  lens,  and  G  is  an  adjustable  slit.  By 
moving  the  inner  tube  back  and  forth,  the  instrument  may 


FIG.  284. 

be  so  focused  that  parallel  rays  will  fall  upon  prism  A.  This 
instrument  has  no  telescope.  By  varying  the  kind  of  glass 
used  in  the  different  prisms,1  as  well  as  their  structure,  the 
deviation  of  light  from  a  straight  path  in  passing  through 
them  is  overcome,  while  the  dispersion  is  preserved.  On 
account  of  the  directness  of  the  path  of  light  through  it,  this 
instrument  is  called  a  direct-vision  spectroscope. 
337.  Bright  line  spectrums. 

Experiment  7. — Open  the  slit  about  one-sixteenth  of  an  inch  wide, 
by  turning  the  milled  ring  M  (Fig.  285),  and  look  through  the  spectro- 
scope at  the  sky  (not  at  the  sun,  for  its  light- 
waves are  too  intense  for  the  eye);  you  will 
see  the  solar  spectrum. 

Experiment  8.  —  Repeat  the  last  experiment 
with  a  candle,  kerosene,  or  ordinary  gas-flame, 
and  you  will  obtain  similar  results. 

1  A  and  C  are  crown-glass,  and  B  is  flint-glass.     See  footnote,  p.  372. 


BRIGHT    LINE    SPECTRUMS.  377 

Experiment  9.  —  Take  a  piece  of   platinum  wire  2  inches  long.     Seal 
one  end  by  fusion  to  a  short  glass  tube  for  a  handle.     Bend  the  wire  at 
a  right  angle.     Dip  a  portion  of  the  wire  into  a  strong 
solution  of  common  salt,  and  support  it  by  a  clamp  in 
the  midst  of  the  almost  invisible  and  colorless  flame  of 
a    Bunsen    burner     (Fig.    286).      Instantly   the    flame 
becomes  luminous  and  colored  a  deep  yellow.    Examine 
it  with  a  spectroscope,  and  you  will  find,  instead  of  a 
continuous  spectrum  beginning  with  red,  only  a  bright, 
narrow  line  of  yellow,  in  the  yellow  part  of  the  spectrum, 
next  the  orange.     Your  spectrum  consists  essentially  of 
a  single1  bright  yellow  line  on  a  comparatively  dark          FIG.  286. 
ground  (see  Sodium,  Plate  I,  frontispiece). 

Experiment  10.  —  Heat  the  platinum  wire  until  it  ceases  to  color  the 
flame,  then  dip  it  into  a  solution  of  chloride  of  lithium,  and  repeat  the  last 
experiment.  You  obtain  a  carmine-tinted  flame,  and  see  through  the 
spectroscope  a  bright  red  line  and  a  faint  orange  line  (see  Lithium,  Plate  I). 

Experiment  11.  —  Use  potassium  hydrate,  and  you  obtain  a  violet- 
colored  flame,  and  a  spectrum  consisting  of  a  red  line  and  a  violet  line 
(the  latter  very  difficult  to  see  even  with  the  best  instruments).  Use 
strontium  nitrate,  and  obtain  a  crimson  flame,  and  a  spectrum  consist- 
ing of  several  lines  in  the  red  and  the  orange  and  a  blue  line  (see  Potas- 
sium and  Strontium,  Plate  I). 

Experiment  12.  —  Use  a  mixture  of  several  of  the  above  chemicals, 
and  you  will  obtain  a  spectrum  containing  all  the  lines  that  characterize 
the  several  substances. 

Every  chemical  compound -used  in  the  above  experiments 
contains  a  different  metal,  e.g.  common  salt  contains  the 
metal  sodium  ;  the  other  substances  used  successively  con- 
tain respectively  the  metals  lithium,  potassium,  and  stron- 
tium. These  metals,  when  introduced  into  the  flame,  are 
vaporized,  and  we  get  their  spectrums  when  in  a  gaseous 
state.  All  incandescent  gases,  unless  under  great  pressure, 
give  discontinuous,  or  bright  line,  spectrums,  and  no  two  gases 
give  the  same  spectrum,. 

1  Spectroscopes  of  higher  dispersive  power  show  that  the  sodium  line  is  really  a 
double  line  divided  by  a  narrow  interval. 

"  It  is  not  a  hypothesis,  but  a  reality,  that  sodium  vapor  has  two  independent 
vibrations,  whose  periods  differ  by  about  F5$cn  of  each  other."  —LORD  KELVIN. 


378  ETHER 

338.  Speetrum  analysis. 

A  vibrating  molecule  embedded  in  ether  emits  waves,  the  length 
of  which  depends  on  the  rate  of  vibration,  and  the  waves  of  different 
lengths  produce  the  different  color  sensations.  Now,  like  a  tuning 
fork,  a  free  molecule  of  every  substance  has  its  own  definite  period 
or  periods  of  vibration,  and  accordingly  sends  out  light  of  a  certain 
definite  color  or  of  a  few  definite  colors,  just  as  the  fork  emits  sound 
of  a  certain  definite  pitch,  with  sometimes  a  few  harmonics.  For 
example,  every  molecule  of  sodium  or  of  lithium  vibrates  in  the 
same  way,  and  always  has  vibrated  in  the  same  way,  whether  it 
exists  in  the  sun,  in  the  earth,  or  in  a  distant  star.  The  same  is 
true  of  every  other  kind  of  matter  ;  each  has  its  own  rates  of  vibra- 
tion, and  hence  each  produces  its  own  bright  line  spectrum  corre- 
sponding with  its  peculiar  rates  of  vibration.  Hence  has  arisen  a 
new  chemical  analysis,  wherein  substances  are  detected  simply  by 
observing  the  rates  of  vibration  of  their  molecules  (i.e.  the  bright 
lines  of  their  spectrums),  a  branch  of  physical  chemistry  called 
spectrum  analysis. 

It  is  only  in  the  gaseous  state,  however,  that  the  molecule  is  free 
to  exhibit  its  special  rate  of  vibration ;  when  they  are  packed  closely 
together  in  a  solid  or  liquid,  their  motions  are  cramped,  their  perio- 
dicity is  lost,  and  all  manner  of  vibrations  are  induced.  Hence 
spectrums  of  solids  and  liquids  are  continuous,  i.e.  the  rates  of 
vibrations  are  so  many  in  number  as  to  leave  no  gaps  in  their 
spectrums. 

Many  chemical  compounds  are  decomposed  into  their  elements, 
and  the  elements  are  rendered  gaseous  at  a  temperature  that  is  at, 
or  below,  the  temperature  necessary  for  incandescence.  In  that 
case  the  spectrum  given  is  the  combined  spectrums  of  the  elements. 
A  compound  gas  that  does  not  suffer  dissociation  at  the  temperature 
of  incandescence  gives  its  own  spectrum,  which  is  generally  totally 
different  from  the  spectrum  of  it»  elements. 

339.  Reversed  or  dark  line  spectrum. 

Experiment  13.  —  Arrange  apparatus  in  a  dark  room  as  in  Fig.  287. 
N  is  the  flange  nozzle  of  a  stereopticon  (p.  432)  containing  only  the  con- 
densing lens ;  T  and  S  are  two  tin  plates,  in  the  latter  of  which  a  slit  is 
cut.  Allow  a  beam  of  calcium  light  to  pass  through  the  slit  in  S,  and 
thence  through  the  converging  lens  L  and  the  prism  P,  and  form  a  spec- 
trum on  a  screen,  H.  Hold  in  the  flame  of  a  Bunsen  burner,  B,  a  pellet 


REVERSED    OR    DARK    LINE    SPECTRUM. 


379 


of  sodium  ;  it  burns  vividly,  and  the  light  has  to  pass  through  the  in- 
tensely yellow  flame.  We  should  naturally  expect  that  the  yellow  of  the 
spectrum  would  now  be  more  intensely  illuminated,  but,  instead,  a  dark 
band  in  the  yellow  now  appears.  It  is  not  really  black,  but  compara- 
tively dark. 

Next  hold  the  plate  T  between  the  burner  and  the  condensers  so  that 
the  calcium  light  may  be  cut  off  from  the  upper  portion  of  the  slit, 
leaving  the  light  from  the  sodium  flame  alone  to  pass  through  this  part 
of  the  slit,  The  spectrum  R  formed  by  this  part  consists  of  a  bright 
yellow  line  on  a  dark  ground,  being  the  radiation  spectrum  of  sodium. 
(It  should  be  borne  in  mind  that  the  image  of  the  slit  is  inverted.)  The 


FIG.  287. 


other  half,  A,  shows  a  dark  line  on  the  continuous  spectrum.  We  thus 
have,  contiguous  to  each  other,  the  bright  line  spectrum  of  sodium  and 
its  reversed,  dark  line,  or  absorption  spectrum.  If  you  use  salts  of  lithium, 
potassium,  strontium,  etc.,  in  a  similar  manner,  you  will  find  in  every 
case  your  spectrum  crossed  by  dark  lines  where  you  would  expect  to  find 
bright  lines. 

It  thus  appears  that  the  vapors  of  different  substances  absorb 
or  quench  the  very  same  rays  that  they  are  capable  of  emitting? 
when  made  self-luminous;  very  much,  it  would  seem,  as  a 
given  tuning-fork  selects  from  various  sounds  only  those  of 


380  ETHER    DYNAMICS. 

a  definite  wave-length  corresponding  to  its  own  vibration- 
period.  The  dark  places  of  the  spectrum  receive  light  in 
full  force  from  the  salted  flame;  but  the  light  is  so  feeble, 
in  comparison  with  those  places  illuminated  by  the  calcium 
light,  that  the  former  appear  dark  by  contrast.  Light  trans- 
mitted through  certain  liquids  (as  sulphate  of  quinine  and 
blood)  and  certain  solids  (as  some  colored  glasses)  produces 
band  spectrums.  These  spectrums  are  obtained  only  when 
light  passes  through  mediums  capable  of  absorbing  rays  of 
certain  wave-length  ;  hence,  they  are  commonly  called  absorp- 
tion spectrums.  Since  a  given  vapor  causes  dark  lines  pre- 
cisely where  it  would  cause  bright  lines  if  it  were  itself  the 
only  radiator  of  light,  dark  line  spectrums  are  frequently 
called  reversed  spectrums.  There  are  then  three  kinds  of 
spectrums :  continuous  spectrums,  produced  by  luminous  solids, 
liquids,  or,  as  has  been  found  in  a  few  instances,  gases  under 
great  pressure  ;  bright  line  spectrums,  produced  by  luminous 
vapors ;  and  absorption  spectrums,  produced  by  light  that  has 
been  sifted  by  certain  mediums. 

340.  Fraunhofer^  s  lines.  —  The  spectrum  of  sunlight  is 
observed  to  contain  a  large  number  of  dark  lines  transverse 
to  its  length.  These  were  first  observed  by  Wollaston  (1802), 
and  were  mapped  by  Fraunhofer  (1814)  who  distinguished 
several  of  the  more  prominent  ones  by  letters  of  the  alpha- 
bet ;  hence  the  dark  lines  of  the  solar  spectrum  have  received 
the  name  of  Fraunhofer 's  lines. 

So  far  as  discovered,  no  two  substances  have  a  spectrum 
consisting  of  the  same  combination  of  lines  ;  and,  in  general, 
different  substances  very  rarely  possess  lines  appearing  to 
be  common  to  both.  Hence,  when  we  have  once  observed  and 
mapped  the  spectrum  of  any  substance,  we  may  ever  after  be 
able  to  recognize  the  presence  of  that  substance  when  emit- 
ting light,  whether  it  is  in  our  laboratory  or  in  a  distant 
heavenly  body. 


FRAUNHOFER'S  LINES.  381 

The  spectroscope,  therefore,  furnishes  us  a  most  efficient 
means  of  detecting  the  presence  (or  absence)  of  any  elemen- 
tary substance,  even  when  it  is  combined  or  mixed  with  other 
substances.  It  is  not  necessary  that  the  given  substance 
should  exist  in  large  quantities  ;  for  example,  the  fourteen- 
millionth  part  of  a  milligram  of  sodium  can  be  detected  by 
the  spectroscope.  Substances  which  are  not  easily  converted 
into  vapors  at  low  temperatures  may  be  placed  between  the 
poles  of  an  electric  battery  or  an  induction  coil.  The  heat 
generated  by  electricity  will  vaporize  most  substances.  Thus 
the  spark  passing  between  two  copper  electrodes  will  vaporize 
a  portion  and  show  the  copper  lines,  between  iron  electrodes 
the  iron  lines,  etc.  After  maps  of  the  spectrum  of  all  known 
substances  have  been  made  out,  if,  on  examination  of  a  com- 
plex substance,  any  new  lines  should  at  any  time  appear  in 
the  spectrum,  it  would  indicate  the  presence  of  a  substance 
hitherto  undiscovered.  It  was  thus  that  the  elements  cae- 
sium, rubidium,  thallium,  and  indium  were  discovered.1 

341.    General  remarks. 

Gases  or  vapors  when  sufficiently  heated  to  become  luminous 
emit,  under  ordinary  pressure,  color  rays  which  are  dispersed  into 
an  interrupted  spectrum  of  bright  lines  ;  with  increasing  pressure 
and  density  these  lines  spread  into  diffuse  luminous  bands,  and 
finally  form  a  continuous  spectrum.  Gases  are  rendered  luminous 
usually  by  passing  electric  sparks  through  glass  tubes  enclosing 
them.  Substances  whose  great  volatility  interferes  by  causing 
evaporation  before  the  substance  attains  the  temperature  of  incan- 

1  Fraunhofer's  lines,  designated  by  letters  of  the  alphabet,  beginning  at  the  red 
end  of  the  spectrum,  have  the  following  wave-lengths,  expressed  in  millionths  of  a 
millimeter  : 

Line.  Wave-length.  Line.  Wave-length. 

A  7621  E2  527.0 

B  688.4  b,  518.3 

C  656.3  F  486.1 

I>,  589.6  G  430.7 

\\  589.0  H,  396.8 

H,  393.3 


382  ETHER    DYNAMICS. 

descence,  such  as  most  metalloids,  give  no  flame  emission  spectrums. 
These  are  commonly  rendered  luminous  in  glass  tubes  called  Pliicker 
tubes  (Fig.  288). 

Colored  liquids  are  usually  placed  in  glass  cells  with  flat  parallel 
sides,  or  of  wedge  shape  so  as  to  allow  the  examination  of  different 
thicknesses  of  the  liquid.     The  cells  are  placed  between      • — . 
a  bright  flame  and  the  slit  (or  better  in  reflected  sunlight),         A^ 
and  the  result  is  absorption  spectrums  of  the  coloring        f    J 
matter,  consisting  of  dark  bands.      Thus  blood  in   its 
normal   or  healthy  state   is  readily   recognized   by  the 
absorption  spectrums  of  its  coloring  matters  and  their 
modifications    by    absorption    of   gases.1     Aniline    blue 
shows  a  Very  dark   absorption   band  from  wave-length 
656  (C)  to  550,  gradually  becoming  lighter  from  there  to 
520  (just  beyond  V). 

The  spectroscope  is  very  useful  to  the  pathologist  in 
examining  diseased  blood,  in  detecting  albumen  in  urine, 
in  investigating  supposed  cases  of  poisoning,  etc.  ;  to  the 
merchant  in  distinguishing  certain  liquids  such  as  wine,  beer,  etc. 
in  the  normal  state  and  the  adulterated  state. 

342.    Solar  and  stellar  chemistry  and  physics. 

The  spectrum  of  iron  has  been  mapped  to  the  extent  of  more 
than  600  bright  lines.  Of  these,  Kirchhoff  succeeded  in  showing 
the  coincidence  of  460  with  dark  lines  of  the  solar  spectrum.  Can 
there  be  any  doubt  of  the  existence  of  iron  in  the  sun  ?  By  exam- 
ination of  the  reversed  spectrum  of  the  sun,  we  are  able  to  deter- 
mine with  certainty  the  existence  there  of  sodium,  calcium,  copper, 
zinc,  magnesium,  hydrogen,  and  many  other  known  substances. 
Again,  from  our  knowledge  of  the  way  in  which  a  reversed  spectrum 
can  be  produced,  we  may  conclude  that  the  sun  consists  of  a  lumi- 
nous solid,  a  liquid,  or  an  intensely  heated  and  greatly  condensed 
gas  (called  a  photosphere),  and  that  this  nucleus  is  surrounded  by  an 
atmosphere  of  cooler  vapor,  in  which  exist  at  least  all  the  substances 

*A  solution  of  fresh  blood  gives  two  easily  distinguishable  dark  bands  in  the 
green.  But  blood  is  capable  of  existing  in  different  stages  of  oxidation  which  are 
distinguishable  by  difference  of  color  and  corresponding  difference  of  spectrum.  By 
means  of  a  microspectroscope  (a  combination  of  microscope  and  spectroscope)  it  is 
claimed  that  the  thousandth  part  of  a  grain  of  blood  is  easy  of  detection,  and  its  pres- 
ence may  be  detected  in  stains  that  have  been  kept  a  very  long  time  ;  hence  this  in- 
strument often  becomes  of  great  importance  in  criminal  trials, 


EFFECT    OF    MOTION    IN    THE   RADIATING   BODY.       38S 

just  named.  The  moon  and  planets  that  are  visible  only  by  reflected 
sun-light  give  the  same  spectrums  as  the  sun,  while  those  that  are 
self-luminous  give  spectrums  which  differ  from  the  solar  spectrum. 

343.  Effect  of  motion  in  the  radiating  body. 

If  the  radiating  body  be  in  motion,  either  to  or  from  the  observer, 
obviously  the  effect  of  this  motion  will  be  to  shorten  the  wave-length 
in  the  former  case  and  to  lengthen  it  in  the  latter  (compare  §173). 
This  will  tend  to  move  the  spectrum  lines  toward  the  more  re- 
frangible end  in  the  first  instance  and  toward  the  less  refrangible 
end  in  the  latter.  Thus  from  the  displacement  of  hydrogen  lines  in 
the  absorption  spectrum  Young  computes  that  the  greatest  speed 
upon  the  sun  observed  by  him  is  400  kilometers  per  second. 
Pickering  (Harvard  Univ.)  has  observed  that  the  k  line  in  the  spec- 
trum of  j8  Aurigae  is  alternately  single  and  double  at  intervals  of 
about  seventeen  hours,  thus  showing  this  star  to  be  double,  each 
part  revolving  about  the  other  in  less  than  four  days  at  a  speed 
of  240  kilometers  per  second. 

The  telespectroscope  (a  combination  of  telescope  and  spectroscope) 
has  disclosed  to  us  a  much-coveted  knowledge  of  the  true  nature, 
chemical  composition,  and  physical  condition  of  those  points  of 
light  called  the  fixed  stars,  immensely  more  remote  and  less  bright 
than  the  planets.  In  like  manner  nebulae,  comets,  and  meteors 
have  been  investigated,  and  valuable  knowledge  has  been  obtained 
as  to  their  physical  constitution. 

344.  Distribution  of  energy  in  the  spectrum.  —  The  energy 
of  ether  waves  is  capable,  as  has  been  before  observed,  of  pro- 
ducing calorific,  luminous,  or  chemical  effects,  according  to 
the  nature  of  the  bodies  upon  which  it  falls.     When  a  sensi- 
tive thermoscope  is  passed  along  the  spectrum,  heat  effects 
are  observed  throughout  the  visible  spectrum,  and  for  con- 
siderable  distances   beyond   at  each  extremity.      All   ether 
waves  are  capable  of  producing  heating  effects. 

It  thus  appears  that  the  solar  spectrum  is  not  limited  to  the 
visible  spectrum,  but  extends  beyond  at  each  extremity,  and 
spectroscopic  analysis,  besides  sifting  the  waves  of  one  color 
from  those  of  another,  is  able  to  sift  out  rays  which  do  not 


384  ETHER    DYNAMICS. 

produce  the  sensation  of  light  from  those  which  do.  Those 
rays  that  lie  beyond  the  red  are  called  the  infra-red  rays,  while 
those  that  lie  beyond  the  violet  are  called  the  ultra-violet  rays. 
The  infra-red  rays  are  of  longer  vibration  period,  and  the 
ultra-violet  of  shorter  period,  than  the  luminous  waves. 

Inasmuch  as  glass  largely  absorbs  the  energy  of  ether  waves  of 
certain  lengths,  it  is  customary  in  studying  heat  spectrums  to  use 
lenses  and  prisms  of  rock  salt,  since  this  substance  transmits  waves 
of  all  lengths  with  great  freedom. 

In  a  prismatic  spectrum  obtained  by  the  use  of  a  rock  salt  prism, 
the  maximum  heating  effect  for  the  solar  spectrum  is  in  the  infra- 
red. Langley  finds,  however,  that  in  the  normal  spectrum  the  maxi- 
mum heating  effect  in  the  solar  radiation  coincides  quite  closely 
with  the  maximum  luminous  effect  which  is  in  the  orange-yellow. 

Chemical  effects  are  produced  by  rays  of  all  refrangibilities. 
A  photograph  can  be  taken  of  all  portions  of  the  visible  spectrum, 
and  the  photographic  spectrum  may  extend  far  beyond  the  visible 
spectrum  in  the  ultra-violet,  and  even  the  infra-red  rays  may  be 
photographed.  Ordinary  silver  salts  are  decomposed  by  rays  ex- 
tending from  the  green  upward,  while  the  decomposition  of  carbon 
dioxide  is  aided  chiefly  by  rays  of  lower  refrangibility. 

345.  Only  one  kind  of  radiation.  —  The  fact  that  radiant 
energy  produces  three  distinct  effects, — viz.  luminous,  heat- 
ing, and  chemical, — has  given  rise  to  a  prevalent  idea  that 
there  are  three  distinct  kinds  of  radiation.1  There  is,  how- 
ever, absolutely  no  proof  that  these  different  effects  are  pro- 
duced by  different  kinds  of  radiation.  Science  recognizes  in 
radiations  no  distinctions  but  periods,  wave  lengths,  and  wave 
forms.  The  same  radiation  that  produces  vision  can  generate 
heat  and  chemical  action.  The  fact  that  the  infra-red  and  ultra- 
violet rays  do  not  affect  the  eye  does  not  argue  that  they  are  of 
a  different  nature  from  those  that  do,  but  it  does  show  that 

1  One  great  service  which  the  diffraction  spectrum  (see  §  361)  has  rendered  to  science 
is  the  abolishment  of  all  these  imaginary  independent  existencies  —  heat,  light,  acti- 
nism, etc.,  and  the  substitution  for  them  of  the  far  simpler  conception  of  vibratory 
motions  of  ether  differing  only  in  rate  of  vibration,  the  diversity  of  effects  produced 
depending  on  the  quality  of  the  surface  on  which  they  fall. 


PHOSPHORESCENCE.  385 

there  is  a  limit  to  the  susceptibility  of  the  eye  to  receive  im- 
pressions from  radiation.  Just  as  there  are  sound-waves  of 
too  long,  and  others  of  too  short  period  to  affect  the  ear,  so 
there  are  ethereal  waves,  some  of  too  long,  and  others  of  too 
short  period  to  affect  the  eye. 

346.  Phosphorescence.  —  There  is  a  class  of  substances  such 
as    the    sulphides    of   calcium,   strontium,   etc.,    which    after 
several  hours'  exposure  to  light-waves  absorb  their  energy 
(i.e.  their  molecules  acquire  sympathetic  vibrations)  without 
becoming  hot,  and  in  return  emit  light-waves,  which  are  quite 
perceptible  in  a  dark  room  for  several  hours  after  the  ex- 
posure.    This  property  of  shining  in  the  dark  after  having 
been  exposed  to  light-waves  is  termed  phosphorescence.     A  so- 
called  luminous  paint  is  prepared  and  applied  to  certain  parts 
of  bodies  that  are  exposed  to  sunshine  during  the  day  ;  at 
night  those   parts  to  which  the  paint  is  applied  are  alone 
luminous.     This  paint  may  be  used  for  a  variety  of  purposes, 
such  as  rendering  luminous  danger. signals,  door  numbers  and 
plates,  etc. 

347.  Fluorescence. 

There  is  another  class  of  substances  which  are  acted  upon  in  a 
somewhat  similar  and  yet  somewhat  different  manner.  The  vibra- 
tions of  the  extremely  small  ether-atoms  may  set  up  in  the  more  pon- 
derous molecules  of  matter  slower  (forced)  vibrations.  We  have  an 
example  of  this  when  light-waves  are  absorbed  by  a  body  and  it  in 
turn  emits  only  the  longer,  invisible  waves.  Much  as  short,  choppy 
waves  acting  upon  a  vessel  anchored  at  sea  impart  a  slower  pitching 
and  rolling  of  the  vessel,  and  these  in  turn  new  and  slower  waves  in 
the  water,  the  invisible  ultra-violet  waves  may  give  rise  to  dis- 
turbances of  the  interior  molecules  of  a  body  impinged  upon,  and 
give  rise  to  other  waves  which  are  not  so  frequent  as  to  be  invisible. 
In  this  case  the  body  emits  light  from  within,  and  in  some  cases 
continues  to  emit  light  for  some  seconds  after  the  light  is  shut  off. 
This  phenomenon  is  known  by  the  name  fluorescence,  from  fluor- 
spar, one  of  the  first  substances  in  which  it  was  observed.  Among 
fluorescent  substances  are  aesculin  (derived  from  the  bark  of  the 


386  ETHER   DYNAMICS. 

horse-chestnut),  quinine  sulphate,  sulphides  of  barium  and  calcium, 
diamond,  uranium  glass,  etc.  These  substances  when  illuminated 
by  certain  rays  of  the  spectrum  in  a  darkened  room  shine  from 
within  with  a  lustre  of  their  own,  each  showing  its  own  special 
color,  a  color  not  by  any  means  the  same  as  the  natural  color  of 
the  body  itself  as  seen  in  the  open  white  light  of  day.  This  is  best 
accomplished  by  means  of  the  light  of  electric  discharges.  For  this 
purpose  solids  are  usually  enclosed  in  the  so-called  Geissler  tubes 
and  an  electric  current  is  passed  through  them. 

348.  Calorescence. 

On  the  other  hand,  slow  waves  may  be  transformed  into  more 
rapid  ones.  A  beam  of  light  passing  through  a  solution  of  iodine 
in  carbon  bisulphide  loses  all  its  visible  rays  and  only  the  long 
infra-red  rays  pass  through.  If  these  be  brought  to  a  focus  by 
means  of  a  lens  upon  a  piece  of  platinum,  the  platinum  will  become 
luminous,  and  the  light  emitted  therefrom  when  examined  by 
means  of  a  prism  shows  a  continuous  spectrum.  This  elevation  in 
the  rank  of  wave-length  is  called  calorescence. 

SECTION  IX. 
COLOR. 

349.  Color  by  absorption.  —  Color  is  a  sensation  ;  it  has  no 
material  existence.      The  term   " yellow  light"   means,  pri- 
marily,   a   particular    sensation ;    secondarily,   it   means   the 
physical  cause  of  this  sensation,  i.e.  a  train  of  ether-waves 
of  a  particular  frequency.     "  All  objects  are  black  in  the 
dark  "  ;  this  is  equivalent  to  saying  that  without  light  there 
is  no  color. 

Experiment  1.  —  By  means  of  a  porte-lumiere  introduce  a  beam  of 
sunlight  into  a  dark  room.  With  the  slit  and  prism  form  a  solar  spec- 
trum. Between  the  slit  and  prism  introduce  a  deep  red  glass ;  all  the 
colors  of  the  spectrum  except  the  red  are  much  reduced  in  intensity. 

It  thus  appears  that  the  color  of  a  colored  transparent 
object,  as  seen  by  transmitted  light,  arises  from  the  unequal 
absorption  of  the  different  colors  of  white  light  incident  upon 


COLOR    BY   ABSORPTION.  387 

it.  A  red  glass  absorbs  less  red  light  than  light  of  other 
colors.  The  color  produced  by  absorption  is  rarely  very 
pure,  the  particular  hue  of  the  transmitted  light  being  due 
merely  to  a  predominance  of  certain  colors,  and  not  to  the 
absence  of  all  others.  As  the  absorbing  layer  is  thicker,  the 
resulting  color  is  purer  but  less  intense. 

Experiment  2.  —  We  have  found  that  common  salt  introduced  into  a 
Bunsen  flame  renders  it  luminous,  and  that  the  light  when  analyzed  with 
a  prism  is  found  to  contain  only  yellow.  Expose  papers  or  fabrics  of 
various  colors  to  this  light  in  a  darkened  room.  No  one  of  them  except 
yellow  exhibits  its  natural  color. 

Experiment  3.  —  Hold  a  narrow  strip  of  red  paper  or  ribbon 1  in  the 
red  portion  of  the  solar  spectrum  ;  it  appears  red.  Slowly  move  it 
toward  the  other  end  of  the  spectrum  ;  on  leaving  the  red  it  becomes 
darker,  and  when  it  reaches  the  green  it  is  quite  black  or  colorless,  and 
remains  so  as  it  passes  the  other  colors  of  the  spectrum.  Repeat  the 
experiment,  using  other  colors,  and  notice  that  only  in  light  of  its  own 
color  does  each  strip  of  paper  appear  of  its  natural  color,  while  in  all 
other  colors  it  is  dark. 

These  experiments  show  that  the  color  of  a  body  seen  by 
light  reflected  from  it  depends  both  upon  the  color  of  the 
light  incident  upon  it  and  upon  the  nature  of  the  body. 

If  a  piece  of  colored  glass,  AB  (Fig.  289),  be  held  near  a 
window  so  as  to  receive,  obliquely,  rays  of  sunlight,  a  portion 
of  the  light  will  be  reflected  by  the  anterior  surface  of  the 
glass,     and,     falling 
upon  the  white  ceil- 
ing,   will    illuminate 
it  with  white  light. 
Another    portion    of 
the  light  will   enter 
the  glass  and  be  re- 
flected from  the  pos- 
terior  surface  ;    this   light,    having    entered   the    glass    and 

1  Care  must  be  exercised  to  select  only  pure  colors. 


388  ETHEK    DYNAMICS. 

traveled  in  it  a  distance  a  little  greater  than  twice  its  thick- 
ness, will  suffer  an  unequal  absorption  of  its  rays,  and  after 
emerging  from  the  glass  will,  if  the  glass  be  blue,  illuminate 
a  neighboring  portion  of  the  ceiling  with  blue  light.  This 
illustrates  the  method  by  which  pigments  afford  color.  Thus, 
the  first  surface  of  a  water-color  drawing  reflects  the  white 
daylight.  Most  of  the  light  reflected  to  the  eye  has,  how- 
ever, passed  through  the  pigment  to  the  white  paper  beneath, 
and  being  reflected  from  this,  again  passes  through  the  layer 
of  pigment  before  reaching  the  eye.  With  less  transparent 
pigments  the  light  may  be  reflected  merely  by  particles  of 
pigment  beneath  the  surface.  The  color  of  paints  and  pig- 
ments is,  therefore,  due  to  the  rays  which  they  absorb  least 
readily.  When  we  paint  our  houses  we  do  not  apply  color  to 
them;  we  apply  substances  which  have  the  property  of  ab- 
sorbing or  subtracting  from  white  light  largely  all  the  colors 
except  those  which  we  would  have  our  houses  appear.  This 
is  technically  called  selective  absorption. 

The  color  of  bodies  thus  depends  generally  upon  their  mo- 
lecular structure.  Different  bodies  quench  different  portions 
of  the  complex  sunlight.  The  unquenched  light  determines 
the  color  of  a  body. 

The  molecular  action  in  the  case  of  absorption  is  this.  The 
molecules  of  the  substance  receiving  incident  light  are  capable  of 
vibrating  in  unison  with  certain  ether  waves.  The  energy  of  cer- 
tain of  the  ether-waves  is  employed  in  setting  up  molecular  vibra- 
tions in  the  substance,  thus  raising  its  temperature,  while  the 
energy  of  waves  of  different  period  is  propagated  through  the  me- 
dium without  producing  this  effect. 

350.    Opalescence.     Sky  colors. 

Experiment  4-  —  Dissolve  a  little  white  castile  soap  in  a  tumbler  of 
water  ;  or,  better,  stir  into  the  water  a  few  drops  of  an  alcoholic  solution 
of  mastic,  enough  to  render  the  water  slightly  turbid.  Place  a  black 
screen  behind  the  tumbler,  and  examine  the  liquid  by  reflected  sunlight, 


MIXING   COLORS.  389 

—  the  liquid  appears  to  be  blue  ;  examine  the  liquid  by  transmitted  sun- 
shine, —  it  now  appears  yellowish  red. 

Experiment  5.  —  Pour  some  of  the  turbid  liquid  into  a  small  test-tube, 
and  examine  it  and  the  tumbler  of  liquid  by  transmitted  light  ;  the  former 
appears  almost  colorless,  while  the  latter  is  deeply  colored. 

When  a  medium  holds  in  suspension  fine  particles  of  mat- 
ter, the  shorter  light-waves  are  most  abundantly  reflected, 
giving  a  blue  color.  The  blue  is  purer  as  the  particles  are 
smaller.  Objects  seen  through  such  mediums  appear  of  the 
complementary  hue  (see  §  354).  This  phenomenon  is  called 
opalescence.  It  accounts  for  the  blue  of  watery  milk,  opa- 
lescent glass,  smoke,  and  the  sky. 

Skylight  is  reflected  light.  The  minute  particles  (of  water, 
probably)  that  pervade  the  atmosphere,  like  the  fine  particles 
of  mastic  suspended  in  the  water,  reflect  blue  light;  while 
beyond  the  atmosphere  is  a  black  background  of  darkness. 
But  we  must  not,  from  this,  conclude  that  the  atmosphere  is 
blue  ;  for,  unlike  blue  glass,  but  like  the  turbid  liquid,  it 
transmits  yellow  and  red  rays  freely,  so  that  seen  by  re- 
flected light  it  is  blue,  but  seen  by  transmitted  light  it  is 
yellowish  red. 

The  remarkable  "yellow  days"  of  the  summer  of  1883  are 
explained  in  this  way.  The  atmosphere  on  this  continent 
was  very  turbid  during  those  days. 

When  the  sun  is  near  the  horizon,  its  rays  travel  a  greater 
distance  in  the  air  to  reach  the  earth  than  when  it  is  in  the 
zenith  (see  Fig.  263)  ;  consequently,  there  is  a  greater  loss  by 
absorption  and  reflection  in  the  former  case  than  in  the  latter. 
But  the  yellow  and  red  rays  suffer  less  destruction,  propor- 
tionally, than  the  other  colors  ;  consequently,  these  colors 
predominate  in  the  morning  and  evening. 

351.  Mixing  colors.  —  A  mixture  of  all  the  prismatic  colors 
in  the  proportion  found  in  sunlight  produces  white.  Can 
white  be  produced  in  any  other  way  ? 


390 


ETHER    DYNAMICS. 


Experiment  6.  — On  a  black  surface,  A  (Fig.  290),  lay  two  small  rec- 
tangular pieces  of  paper,  one  yellow  and  the  other  blue,  about  two  inches 
apart.  In  a  vertical  position  between  these  papers, 
and  from  3  inches  to  6  inches  above  them,  hold  a  slip 
of  plate  glass,  C.  Looking  obliquely  down  through 
the  glass  you  may  see  the  blue  paper  by  transmitted 
light-waves  and  the  yellow  paper  by  reflection.  That 
is,  you  see  the  object  itself  in  the  former  case,  and 
the  image  of  the  object  in  the  latter  case.  By  a  little 
manipulation  the  image  and  the  object  may  be  made 
to  overlap  each  other,  when  both  colors  will  ap- 
parently disappear,  and  in  their  place  the  color  which 
is  the  result  of  the  mixture  will  appear.  In  this  case 
it  will  be  white,  or  rather,  gray,  which  is  white  of  a 
low  degree  of  luminosity.  If  the  color  be  yellowish,  lower  the  glass ;  if 
bluish,  raise  it. 

Experiment  7.  —  With  the  rotating  apparatus,  rotate  the  disk  (Fig.  291) 
which  contains  only  yellow  and  blue.  The  colors  (i.e.  the  sensations)  so 
blend  in  the  eye  as  to  produce  the  sensation  of  gray. 

Fig.  292  represents  "Newton's  disk."  which  contains  the 
seven  prismatic  colors  arranged  in  a  proper  proportion  to 
produce  gray  when  rotated. 


FIG.  290. 


FIG.  291. 


FIG.  292. 


FIG.  293. 


In  like  manner,  you  may  produce  white  by  mixing  purple 
and  green ;  or,  if  any  color  on  the  circumference  of  the  circle 
(see  Complementary  Colors,  Plate  I)  be  mixed  with  the  color 
exactly  opposite,  the  resulting  color  will  be  white.  Again, 
the  three  colors,  red,  green,  and  violet,  arranged  as  in  Fig. 
293,  with  rather  less  surface  of  the  green  exposed  than  of 


MIXING    PIGMENTS.  391 

the  other  colors,  will  give  gray.  Green  mixed  with  red, 
in  varying  proportions,  will  produce  any  of  the  colors 
in  a  straight  line  between  these  two  colors  in  the  diagram 
(Plate  I);  green  mixed  with  violet  will  produce  any  of  the 
colors  between  them  ;  and  violet  mixed  with  red  gives 
purple. 

All  colors  are  represented  in  the  spectrum,  except  the 
purple  hues.  The  latter  form  the  connecting  link  between 
the  two  ends  of  the  spectrum.  Our  color  chart  (Plate  I)  is 
intended  to  represent  the  sum  total  of  all  the  sensations  of 
color.  By  means  of  this  chart  we  may  determine  the  result 
of  the  (optical)  mixture  of  any  two  colors,  as  follows  :  Find 
the  places  occupied  upon  the  chart  by  the  two  colors  which 
are  to  be  mixed,  and  unite  the  two  points  by  a  straight  line. 
The  color  produced  by  the  mixture  will  invariably  be  found 
at  the  center  of  this  line. 

352.    Mixing  pigments. 

Experiment  8.  —  Mix  a  little  of  the  two  pigments,  chrome  yellow  and 
ultramarine  blue,  and  you  obtain  a  green  pigment. 

The  last  three  experiments  show  that  mixing  certain  colors, 
and  mixing  pigments  of  the  same  name,  may  produce  very 
different  results.  In  the  first  experiments  you  mixed  colors  ; 
in  the  last  experiment  you  did  not  mix  colors,  and  we  must 
seek  an  explanation  of  the  result  obtained.  If  a  glass  vessel 
with  parallel  sides  containing  a  blue  solution  of  sulphate  of 
copper  be  interposed  in  the  path  of  the  light-waves  which 
form  a  solar  spectrum,  it  will  be  found  that  the  red,  orange, 
and  yellow  waves  are  cut  out  of  the  spectrum,  i.e.  the  liquid 
absorbs  these  waves.  And  if  a  yellow  solution  of  bichromate 
of  potash  or  picric  acid  be  interposed,  the  blue  and  violet 
waves  will  be  absorbed.  It  is  evident  that,  if  both  solutions 
be  interposed,  all  the  colors  will  be  destroyed  except  the 
green,  which  alone  will  be  transmitted  ;  thus  :  — 


392 


ETHEK    DYNAMICS. 


Cancelled  by  the  blue  solution, 
Cancelled  by  the  yellow  solution, 
Cancelled  by  both  solutions, 


G  B  V. 

R  O  Y  G  $  /  . 

$  0  y  G  jfi  /. 


In  a  similar  manner,  when  white  light  strikes  a  mixture  of 
yellow  and  blue  pigments  on  the  palette,  it  penetrates  to  some 
depth  into  the  mixture  ;  and,  during  its  passage  in  and  out, 
all  the  colors  except  the  green  are  destroyed  ;  so  the  mixed 
pigments  necessarily  appear  green.  But  when  a  mixture  of 
yellow  and  blue  waves  enters  the  eye,  we  get,  as  the  result 
of  the  combined  sensations  produced  by  the  two  colors,  the 
sensation  of  white  ;  hence  a  mixture  of  yellow  and  blue  gives 
white. 

The  color  square  3  (Plate  I)  represents  the  result  of  the 
mixture  of  pigments  1  and  2  ;  while  4  represents  the  result 
of  the  optical  mixture  of  the  same  colors. 

353.    Theories  of  color  vision. 

Brewster  (1831)  presented  the  hypothesis  that  all  colors  are  formed 
by  the  union  of  three  primaries,  —  red,  yellow,  and  blue,  —  which 
together  compose  white  light,  and  give,  by  combinations  in  twos, 
the  hues,  orange,  green,  purple,  etc.  This  hypothesis  was  based  on 
the  mixing  of  pigments.  But  the  actual  addition  of  colors  does  not 
give  the  same  result  as  the  mixing  of  pigments,  as  has  been  shown. 

The  generally  accepted  theory  of  color-vision  is  that  of  Dr.  Young 
(1801-2),  verified  by  Maxwell  and  Helmholtz.  It  supposes  the  ex- 
istence of  three  color  sensations,  red,  green,  and  violet.  These  ex- 
cited simultaneously, 
and  with  proper  in- 
tensities, produce  the 
sensation  of  white 
light.  Combined  in 
twos,  they  produce 
the  remaining  color 
sensations.  Thus  red 


B 


E 
FIG. 


294. 


and  green  sensations 

combined  give  yellow 

or  orange  ;  green  and  violet  give  blue,  etc.     The  longer  light-waves 

excite  the  sensation  of  red  ;  together  with  those  somewhat  shorter. 


COMPLEMENTARY    COLORS.  393 

they  excite  both  red  and  green,  thus  giving  yellow,  and  so  on. 
Strictly  speaking,  light- waves  of  any  length  excite  all  three  sensa- 
tions ;  but  usually  either  one  or  two  of  them  greatly  predominate. 

The  relative  intensities  of  the  various  color-sensations  throughout 
the  spectrum  as  obtained  from  actual  measurement  by  Maxwell  are 
shown  in  Fig.  294. 

354.    Complementary  colors. 

Experiment  9.  —  On  a  piece  of  gray  paper  lay  a  circular  piece  of  blue 
paper  15  mm  in  diameter.  Attach  one  end  of  a  piece  of  thread  to  the 
colored  paper,  and  hold  the  other  end  in  the  hand.  Place  the  eyes  with- 
in about  15  cm  of  the  colored  paper,  and  look  steadily  at  the  center 
of  the  paper  for  about  fifteen  seconds  ;  then,  without  moving  the  eyes, 
suddenly  pull  the  colored  paper  away,  and  instantly  there  will  appear  on 
the  gray  paper  an  image  of  the  colored  paper,  but  the  image  will  appear 
to  be  yellow.  This  is  usually  called  an  after-image.  If  yellow  paper  be 
used,  the  color  of  the  after-image  will  be  blue ;  and  if  any  other  color 
given  in  the  diagram  (Plate  I),  the  color  of  its  after-image  will  be  the 
color  that  stands  opposite  to  it. 

This  phenomenon  is  explained  as  follows  :  When  we  look 
steadily  at  blue  for  a  time,  the  eyes  become  fatigued  by  this 
color,  and  less  susceptible  to  its  influence,  while  they  are  fully 
susceptible  to  the  influence  of  other  colors  ;  so  that  when  they 
are  suddenly  brought  to  look  at  white,  which  may  be  regarded 
as  a  compound  of  yellow  and  blue,  they  receive  a  vivid  im- 
pression from  the  former,  and  a  feeble  impression  from  the 
latter  ;  hence  the  predominant  sensation  is  yellow.  Any  two 
colors  which  together  produce  white  are  said  to  be  comple- 
mentary to  each  other.  The  opposite  colors  in  the  diagram 
(Plate  I)  are  complementary  to  one  another. 

The  complement  of  green  is  purple,  —  a  compound  color 
not  existing  in  the  spectrum. 

The  eye  gives  no  direct  knowledge  that  the  composition  of 
light  produces  the  sensation  of  white.  Whether  this  sensa- 
tion is  produced  by  the  coexistence  of  all  the  rays  of  the 
visible  spectrum,  by  a  combination  of  light  of  two  comple- 


394  ETHER    DYNAMICS. 

mentary  colors,  or  by  a  mixture  of  rays  of  the  three  primary 
colors,  can  be  determined  only  by  some  process  of  physical 
analysis. 

355.  Effect  of  contrast.  —  When  different  colors  are  seen  at 
the  same  time,  their  appearance  differs  more  or  less  from  that 
observed  when  they  are  seen  separately.     Thus  a  red  object 
(e.g.  a  red  rose)  appears  more  brilliant  if  a  green  object  be 
seen  in  juxtaposition  with  it.     Such  effects  are  said  to  be  due 
to  contrast. 

When  any  two  colors  given  in  the  circle  (Plate  I)  are 
brought  in  contrast,  as  when  they  are  placed  next  each 
other,  the  effect  is  to  move  them  farther  apart  in  the  color 
scale.  For  example,  if  red  and  orange  be  brought  in  con- 
trast, the  orange  assumes  more  of  a  yellowish  hue,  and  the 
red  more  of  a  purplish  hue.  Colors  that  are  already  as  far 
apart  as  possible,  e.g.  yellow  and  blue,  do  not  change  their 
hue,  but  merely  cause  each  other  to  appear  more  brilliant. 

356.  Color-blindness.  —  In  this  defect  in  vision,  one  of  the 
three  color  sensations  is  either  wanting  or  deficient,  usually 
that  of  red  ;  so  that  the  colors  perceived  are  reduced  to  those 
furnished  by  the  remaining  two  sensations,  viz.,  green  and 
violet.     This  causes  the  red-blind  person  to  confound  reds, 
greens,  and  grays.     In  some  rare  cases  the  sensation  of  green 
or  violet  is  the  one  deficient. 


SECTION  X. 

INTERFERENCE    AND    DIFFRACTION. 

We  have  already  studied  wave  interference  in  the  case  of 
sound  (see  §  178),  and  must  recall  that  two  sets  of  sound- 
waves may  neutralize  each  other  and  produce  silence.  As 
an  example,  we  cite  the  phenomenon  of  beats,  in  which  the 
alternate  increase  and  diminution  of  intensity  is  due  to  the 


YOUNG'S  THEORY.  395 

interference  of  two  sets  of  sound-waves  in  the  same  and  oppo- 
site phases  respectively.  If  radiation  be  a  wave  motion, 
similar  phenomena  ought  to  occur  under  proper  conditions. 

357.  Young's  theory.  —  The  earliest  authentic  experiments 
on  the  interference  of  light-waves  were  made  by  Dr.  Young 
in  1801.  He  admitted  a  beam  of  sunlight  into  a  dark 
chamber  through  a  very  narrow  aperture,  and  in  its  path 
placed  a  screen  having  two  very  small  openings  quite  near 
together.  When  the  two  overlapping  pencils  from  these 
openings  were  made  to  fall  on  a  white  screen  there  appeared 
a  series  of  bands  alternately  bright  and  dark,  which  disap- 
peared when  one  of  the  holes  was  covered. 

Although  Young  ascribed  this  phenomenon  to  interference, 
and  explained  it  very  satisfactorily,  with  the  wave  theory  as 
a  basis,  his  views  were  by  no  means  universally  accepted. 

Grimaldi,  nearly  a  century  and  a  half  before,  had  noticed  light 
and  dark  fringes  at  the  edges  of  shadows  of  small  opaque  bodies 
placed  in  the  path  of  sunlight  admitted  through  a  small  hole.  This 
action  was  called  diffraction  (see  §  360),  and  was  afterwards  studied 
by  Newton.  In  view  of  the  emission  theory,  the  phenomenon  was 
explained  by  assuming  that  the  light  particles  experience  an  at- 
tractive or  repellent  force  as  they  come  near  the  edges  of  bodies. 
Believers  in  the  latter  theory  then  contended  that  Young's  experi- 
ment was  simply  one  of  diffraction. 

To  remove  these  objections  it  was  necessary  to  devise  means  of 
producing  the  same  result,  but  entirely  independently  of  apertures 
and  opaque  bodies.  This  was  first  done  by  Fresnel,1  who  contrived 
two  most  ingenious  experiments  for  producing  the  light  and  dark 
bands,  in  which  the  results  could  be  accounted  for  only  by  assuming 
Young's  theory  of  interference  to  be  correct. 

Let  us  now  consider  what  was  observed  by  Young.  A  and  B 
(Fig.  295)  are  two  illuminated  apertures  very  near  together,  and 
emitting  waves  in  all  directions.  When  these  two  sets  of  waves 
arrive  at  any  point  P  on  the  screen,  they  will  be  in  the  same  phase 
only  if  the  distance  of  P  from  one  of  the  sources,  say  B,  is  one  or 

1  A  full  account  of  Fresnel's  experiments  is  given  in  "  The  Theory  of  Light,"  by 
Preston,  §§  86,  87 


396 


ETHER    DYNAMICS. 


more  complete  wave-lengths  more  than  the  distance  PA.  In  this 
event  the  two  waves  will  conspire  to  increase  the  illumination  at  P, 
and  this  point  will  be  on  a  bright  band. 

On  the  other  hand,  if  P  B  -  P  A  be  equal 
to  a  half  wave-length  or  any  odd  number  of 
half  wave-lengths,  the  waves  from  A  and  B 
will  arrive  at  P  in  exactly  opposite  phases    A 
and  destroy  one  another,  and  P  will  be  a    0 
point  on  a  dark   band.      At  intermediate    B 
positions  for  P,  P  B  -  P  A  will   not  equal 
any   whole   number  of    half  wave-lengths, 
and  hence  the  waves  will  meet  in  neither 
the  same  nor  opposite  phases,  and  the  il- 
lumination at  P  will  be  intermediate  in  its 
intensity  between  that  of  the  brightest  and 


FIG.  295. 


darkest  points.     Thus  the  bands  will  shade  off  imperceptibly  into 
one  another. 

In  the  above  discussion  we  have  assumed  the  light  to  be  mono- 
chromatic, i.e.  all  of  the  same  wave-length.  Let  O  M  be  a  perpen- 
dicular to  the  screens  half  way  between  A  and  B ;  then  the  system 

of  bands  evidently  is 
arranged  symmetrical- 
ly about  M,  this  point 
being  on  a  bright  band. 
It  is  easy  to  see  that 
the  distance  of  any 
given  band  from  M 
bears  a  simple  relation 
to  the  wave-length, 
and  hence  the  bands  will  be  closer  together  for  short  waves  than  for 
long  ones,  as  shown  in  Fig.  296. 

If  composite  light  be  used,  we  should  expect  the  bands  to  be  colored, 
which  is  the  case  for  a  few  of  them  near  the  central  band,  which  is 
white  ;  the  edges  nearer  M  are  blue,  while  the  outer  edges  are  red. 
As  each  color  gives  rise  to  a  separate  system  of  bands,  the  red 
ones  being  broadest  and  the  violet  ones. narrowest,  it  will  happen 
that  after  a  few  alternations  a  red  band  and  a  violet  one  will  fall  at 
the  same  place ;  or  the  dark  spaces  of  one  system  will  be  rilled  by 
the  bright  parts  of  another.  Soon,  then,  as  we  recede  from  M,  the 
bands  become  less  distinctly  marked,  and  finally  merge  into  one 
another  and  fade  into  uniform  illumination. 


FIG.  296. 


COLORS  OF  THIN  PLATES.  397 

358.  Colors  of  thin  plates.  —  Everybody  is  familiar  with 
the  beautiful  color  effects  produced  when  ordinary  white  light 
falls  upon  a  thin  film  of  a  transparent  substance,  such  as  a 
soap  bubble  or  a  film  of  oil  on  water.     This  is  a  case  of  inter- 
ference.    Some  of  the  light  comes  to  the  eye  reflected  from 
the  front  or  nearer  surface  of  the  film ;  another  portion  has 
entered  the  medium  and  been  reflected  from  the  back  surface. 
When  it  emerges,  it  has  been  retarded  an  amount  depending 
on  the  distance  it  has  traveled  in  the  film.     We  might  expect 
that  if  the  retardation  were  an  even  number  of  half  wave- 
lengths, the  two  portions  of  light  would  be  in  a  condition  to 
interfere  in  the  same  phase,  and  that  the  effect  would  be 
increased ;  while  if  the  retardation  were  an  odd  multiple  of 
half  wave-lengths,  the  interference  would  be  destructive,  and 
darkness  would  result. 

The  fact  is  exactly  the  reverse  of  this,  since  by  the  act  of 
reflection  in  the  denser  medium  the  phase  of  the  wave  is 
reversed  and  the  result  is  as  if  the  wave  had  been  retarded 
another  half  wave-length. . 

If  the  eye  view  such  a  film  in  monochromatic  light,  the 
portion  entering  the  film  will  be  retarded  varying  amounts 
depending  on  the  angle  of  incidence  and  on  the  thickness. 
The  film  will,  therefore,  be  crossed  by  bright  and  dark 
bands. 

If,  however,  composite  light  be  used,  cooperative  or  de- 
structive interference,  evidently  cannot  take  place  for  the 
different  colors  at  the  same  points,  and  the  familiar  iris- 
colored  bands  result. 

Experiment  1.  —  Press  firmly  together  two  polished  pieces  of  thick  plate 
glass.  A  number  of  colors  will  be  seen  arranged  in  a  certain  order,  and 
forming  curves  more  or  less  regular  around  the  point  of  pressure.  Ex- 
plain. 

359.  Nen'ton'x   ft  >/(/$. 

Newton's    method   of  studying   these   colors   was    very   simple 
and  effective,  and  the  phenomena  exhibited  are  known  as  "New- 


398  ETHER    DYNAMICS. 

ton's  rings."  If  a  convex  lens  of  very  small  curvature  be  placed 
firmly  upon  a  piece  of  plate  glass  (Fig.  297)  the  film  of  air  between 
the  two  increases  in  thickness  from  the  center  radially,  and  hence 


FIG.  297.  FIG.  298. 

beautiful  circular  interference  bands  are  shown,  having  the  point 
of  contact  as  their  center  (Fig.  298). 

360.  Diffraction. 

This  phenomenon,  first  observed  by  Grimaldi,  and  already  referred 
to  (see  §357),  occurs  when  light  passes  through  a  very  narrow  aper- 
ture or  close  to  the  edge  of  an  opaque  body. 

Newton's  strong  reason  for  rejecting  the  wave  theory  was  that 
light,  as  he  supposed,  did  not  go  round  corners  as  sound  does. 
Closer  examination,  however,  shows  that  the  cases  are  similar  if 
consistent  conditions  be  maintained.  Light  really  does  bend  round 
corners,  while  on  the  other  hand,  well  defined  sound  shadows  may 
be  cast  by  sounds  of  sufficiently  short  wave-length.  In  other  words 
sound  bends  round  corners  very  much  more  readily  than  light, 
merely  because  its  wave-length  is  so  much  greater  in  comparison 
with  the  size  of  the  obstacle. 

The  true  explanation  of  diffraction  phenomena  was  given  by 
Fresnel,  who  attributed  them  to  the  mutual  interference  of  the 
secondary  wavelets  which  diverge  from  the  primary  or  main  wave- 
front  as  it  meets  the  obstacle  or  edges  of  the  aperture  ;  just  as  the 
cases  of  interference  previously  described  are  due  to  the  mutual  in- 
terference of  two  waves.  For  a  fuller  description  of  the  cases  of 
diffraction  and  their  treatment,  the  student  is  referred  to  special 
works  on  optics. 

361.  The  Diffraction   Grating.1 

When  a  distant  source  of  light  is  viewed  through  a  system  of  very 
narrow  rectangular  openings,  a  central  image  is  seen,  and  on  either 
side  of  it  there  are  several  highly  colored  spectral  images,  increasing 

*For  a  more  complete  treatment  of  gratings,  see  Theory  of  Light,  by  Preston. 


THE   DIFFRACTION    GRATING.  399 

in  breadth  but  diminishing  in  brightness  as  they  recede  from  the 
center.  A  device  like  the  above  is  known  as  a  diffraction  grating, 
and  may  be  produced  by  ruling  with  a  diamond  fine  lines  on  a 
piece  of  glass.1  The  lines  form  the  opaque  portions  of  the  grating, 
while  the  spaces  between  them  are  the  slits  through  which  the  light 
passes.  The  effect  is  most  marked  when  the  opaque  parts  and 
transparent  parts  are  equal. 

A  magnified  section  of  a  grating  perpendicular  to  the  lines  is 
shown  in  Fig.  299.  Let  a  b.  represent  a  line  and  adjacent  slit  in 
such  a  position  with 
reference  to  the  point 
P,  where  the  eye  is 
placed,  that  P6-P« 
equals  one  wave- 
length. It  is  clear 
that  the  portion  of  the 
incident  wave  (sup- 
posed to  be  homoge- 
neous) corresponding 
to  a  6  may  be  divided 
into  two  nearly  equal 
parts  which  would  de- 
structively interfere  at  FlG 
P  if  the  grating  were 

not  present.  The  effect  of  the  grating  then  is  to  intercept  one  part 
of  these  interfering  portions  and  enable  the  other  to  become  visible. 
A  bright  band  will  then  be  seen  in  the  direction  P  6. 

The  same  will  happen  for  all  similar  parts  of  the  grating  provided 
the  distances  of  their  extremities  from  P  differ  by  a  whole  number 
of  wave-lengths.  Thus  there  will  appear  a  succession  of  bright 
bands  at  increasing  angular  distances  from  P  M.  It  should  be 
noticed  in  studying  this  figure  that  a  6  is  extremely  small  compared 
with  P  M,  and  therefore  the  figure  is  necessarily  distorted  for 
convenience. 

If  the  light  incident  on  the  grating  be  composite,  evidently  the 
angle  a,  indicating  the  direction  from  P  M  of  the  bright  band,  will 
be  less  for  the  short  waves  than  for  the  long  ones.  Therefore  in 


*Many  of  the  fine  gratings  of  Rowland  have  20,000  lines  to  the  inch.  These,  how- 
ever, are  now  usually  ruled  on  speculum  metal,  as  glass  is  apt  to  injure  the  diamond 
point. 


400 


ETHER    DYNAMICS. 


this  case  the  resulting  band  will  be  colored  —  the  inner  edge  blue, 
the  outer  one  red,  the  portion  lying  between,  yellow  and  green. 

Such  a  phenomenon  is  called  a  diffraction  spectrum.  It  is  what 
is  known  as  a  normal  spectrum,  because  it  exhibits  the  colors,  or 
Fraunhofer  lines  which  locate  them,  always  in  their  true  order  and 
separated  by  spaces  bearing  a  simple  relation  to  their  wave-lengths. 

This  is  not  the  case  in  spectrums  produced  by  refraction.  The 
rays  at  the  red  end  are  crowded  together  and  condensed  out  of  all 

2i   V  D  K  F  G  H 


BC 


E 


G  II 

FIG.  300. 


proportion  to  those  at  the-violet  end ;  i.e.  a  given  difference  in  wave- 
length causes  a  much  greater  separation  in  the  more  refrangible  parts. 
This  is  called  irrationality  of  dispersion.  It  is  exhibited  variously  by 
different  substances.  Fig.  300  shows  the  positions  of  the  principal 
Fraunhofer  lines  as  given  with  prisms  (1)  of  flint  glass,  and  (2)  of 
crown  glass,  having  the  same  refracting  angle.  The  difference 


A  a  23  c 


E  b 


II1  II- 


[ 

8)0  7|5    7|0     6|5 
7[5 


15 


4> 


A          U            ]{      <J                      D                  } 

'  i>          1 

G    h 

1  J 

FIG.  301. 

between  a  normal  or  diffraction  spectrum  and  a  prismatic  one  may 
be  understood  by  a  glance  at  Fig.  301.  The  scales  between  the 
spectrums  indicate  the  wave-lengths  in  hundred  thousandths  of  a 
millimeter. 

The  grating  furnishes  a  simple  means  of  measuring  wave-length. 


-JOA-BJ    9JOUJ    SUOT4T.pUOD    9q^   9.IB    lUOpU9}SUlJ3    \[V    UT   9SJ9    9J9qA\ 
»TT1    TO    sAm    9TT1    93UJS    *10EI    UT    'DU 


REFLECTION    GRATINGS.  401 

Referring  again  to  Fig.  299,  in  which  P  b  is  the  direction  of  the 
first  bright  band,  we  see  that  the  triangles  6  a  k  and  6PM  are 
very  nearly  similar  (a  k  being  a  very  short  arc  practically  per- 
pendicular to  P6).  Then  ||=  ||  =  sin  a  ;  or  bk  =  a  6  sin  a. 

But  6  A;  is  one  wave-length,  X,  and  a  b  is  -  where  n  is  the  number 

n 

of  lines  per  unit  of  length  on  the  grating  ;  hence  X  =  -  sin  a. 

Experiment  2.  —Introduce  a  borax  bead  into  the  flame  of  a  Bunsen 
burner,  and  place  them  near  the  wall  of  a  darkened  room.  From  a 
distance  of  six  or  eight  meters,  view  the  flame  through  a  grating 
(one  having  from  one  to  two  thousand  lines  to  the  centimeter  pre- 
ferred), holding  it  perpendicular  to  the  line  of  sight  and  with  the 
rulings  vertical.  Note  the  position  on  the  wall  of  the  first  image  of 
the  flame,  and  measure  in  centimeters  its  distance  from  the  flame. 
This  divided  by  the  distance  from  the  point  of  observation  to  the 
image  will  be  sin  a.  (In  practice  it  is  found  to  be  sufficiently 
accurate  to  measure  from  the  point  of  observation  directly  to  the 
burner.)  If  we  divide  sin  a  by  the  number  of  lines  per  centimeter 
on  the  grating,  the  result  will  be  the  wave-length  in  centimeters 
for  sodium  light. 

362.    Reflection  gratings. 

Spectrums  similar  to  those  already  described  may  be  produced 
by  reflection  from  a  polished  surface  (usually  of  speculum  metal) 
finely  ruled  with  paral- 
lel grooves.1 

The  beautiful  colors 
exhibited  by  the  pol- 
ished surface  of  mother- 
of-pearl,,  by  the  feathers 

of    certain    birds,    and  %^    ' /^ Grating-Spectroscope 

other  striated  surfaces, 

are  due  to  wave  inter-  (    \     ]         1  coiitmator 

ference.       This     was  V 


demonstrated  in  a  strik-  Grating 

ing  way  by  Sir  David  FlG<  302' 

Brewster,  by  taking  an  impression  of  the  surface  in  wax,  when  the 

indented  wax  showed  all  the  colors  of  the  original  surface. 

;.  302  represents  a  sectional  view  of  a  grating  spectroscope. 


402  ETHER   DYNAMICS. 

SECTION  XL 

DOUBLE    REFRACTION    AND    POLARIZATION    OF    LIGHT. 

363.  Double  refraction.  —  We  have  hitherto  assumed  that  a 
ray  of  light  incident  upon  a  transparent  body  is  refracted 
according  to  the  law  of  sines.  This  is  the  case  when  the 
transparent  body  is  isotropic,  i.e.  having  the  same  properties 
in  all  directions.  There  are  numerous  transparent  substances 
which  fulfil  this  condition  at  least  approximately,  such  as 
fluids,  well  annealed  glass,  etc.  On  the  other  hand,  there  are 
numerous  transparent  substances  for  which  the  law  of  sines 
does  not  hold.  When  a  ray  of  light  enters  such  a  body  it  is 
split  into  two  rays,  and  this  law  does  not  hold  for  both  these 
resulting  rays;  sometimes  it  does  not  hold  for  either  ray. 
This  gives  rise  to  a  group  of  phenomena  known  by  the  term 
double  refraction,  and  the  substances  which  affect  light  in  this 
manner  are  called  doubly  refracting  substances.  These  include 
various  crystals,  animal  substances 
such  as  horn  and  shells,  vegetable 
substances  such  as  resins  and  gums, 
and  certain  artificial  substances  such 
as  jellies  and  un annealed  glass. 

Experiment  1.  —  Through  a  card  make 
a  pin-hole,  and  hold  the  card  so  that  you 
can  see  skylight  through  the  hole.  Now 
bring  a  crystal  of  Iceland  spar  *  (Fig.  303) 
between  the  eye  and  the  card,  and  look  at 
the  hole  through  two  parallel  surfaces  of 
the  crystal.  There  will  appear  to  be  two 

holes,  with  light  shining  through  each.  Cause  the  crystal  to  rotate  in  a 
plane  parallel  with  the  card,  and  one  of  the  holes  will  appear  to  remain 
nearly  at  rest,  while  the  other  revolves  around  the  first. 

1  This  crystal,  sometimes  called  calcite  or  calc-spar,  is  found  most  abundantly  in 
Iceland.  It  exhibits  the  property  of  double  refraction  very  clearly,  and  by  means  of 
it  this  property  was  first  discovered.  By  cleavage  it  can  always  be  brought  into  the 
form  represented  by  the  diagram,  which  is  called  a  rhomb. 


DOUBLE    REFRACTION. 


403 


FIG.  304. 


A  ray  of  light,  PQ,  immediately  on  entering  the  crystal  is  divided  into 
two  parts,  one  of  which,  QO,  obeys  the  regular  law  of  refraction ;  the 
other,  QE,  does  not.  The  former  is  called  the  ordinary  ray ;  the  latter, 
the  extraordinary  ray.  In  all  crystals  which 
produce  this  phenomenon  there  is  one  direction, 
and  in  some  there  are  two,  in  which,  if  an  object 
be  looked  at  through  the  crystal,  it  does  not  ap- 
pear double.  If  all  the  edges  of  a  crystal  of 
Iceland  spar  (Fig.  304)  be  equal,  and  the  line  con- 
necting the  two  opposite  obtuse  solid  angles,  AB, 
be  cut  near  each  extremity  by  a  plane  perpendicular  to  it,  objects  viewed 
in  this  line,  or  in  any  line  parallel  with  it,  do  not  appear  double. 

In  every  direction  in  which  one  looks  through  the  crystal, 
except  that  parallel  to  AB,  objects  seen  through  it  appear 
double  (see  Fig.  305).  The  line  AB  is  called  the  optic  axis  of 
the  crystal,  and  is  a  line  around  which  the  molecules  of  the 
crystal  appear  to  be  arranged  symmetrically.  A  crystal  is 
called  uniaxial  when  it  has  only  one  optic  axis,  and  biaxial 


FIG.  305. 

when  it  has  two  such  axes.  A  plane  parallel  to  this  axis  and 
perpendicular  to  one  of  the  rhombic  faces  of  the  crystal  is 
called  &  principal  section.  The  two  rays  travel  with  unequal 
speeds  in  the  crystal  in  all  directions  except  in  the  direction 
of  the  optic  axis  of  the  .crystal. 

The  property  of  double  refraction  may  be  imparted  per- 
manently or  transiently  to  certain  substances  which  do  not 
naturally  possess  it.  Glass  may  be  given  thi.  power  by 
heating  different  parts  unequally,  and  also  by  compression 
and  bending. 


404  ETHER    DYNAMICS. 

364.  Nicol  prism. 

For  certain  purposes,  such  as  are  indicated  in  §  371,  it  is  best  to 
allow  only  one  of  the  two  rays  to  leave  the  prism  (that,  namely,  in 
the  direction  of  the  incident  light),  and  to  elimi- 
nate the  other.  The  Nicol  prism  consists  of  a 
crystal  of  Iceland  spar  divided  diagonally,  as 
a  6  (Fig.  306),  the  two  surfaces  being  cemented 
together  with  Canada  balsam.  All  the  faces 
of  the  prism  are  painted  black  except  the  two 
end  faces.  The  extraordinary  ray,  falling 
upon  the  transparent  balsam  at  an  angle  less 
than  the  critical  angle,  passes  through  it,  but 
the  more  refracted  (or  ordinary)  ray  meets  the 
balsam  at  an  angle  greater  than  the  critical 
angle,1  and  is  therefore  totally  reflected, 
thrown  to  one  side  of  the  prism,  and  absorbed 
FIG.  306.  by  the  black  paint. 

365.  Polarization  of  light  by  double  refraction.  —  On  exami- 
nation of  the  two  rays  resulting  from  splitting  a  single  ray 
by  double  refraction,  it  is  found  that  each  is  unlike  a  ray  of 
common  light,  that  each  has  properties  with  respect  to  a  fixed 
direction,  and  that  these  fixed  directions  for  the  two  rays  are 
at  right  angles  to  each  other.     In  short,  a  beam  of  light  thus 
treated  is  not  alike  upon  all  sides,  but  has  certain  relations  to 
surrounding  space  other  than  direction.     This  property  can 
be  given  to  light  in  various  ways.     To  this  phenomenon,  how- 
ever produced,  has  been  given  the  name  polarization? 

Slices  of  crystal  of  the  mineral  tourmaline,  cut  in  planes 
parallel  with  their  axes,  are  prepared  and  sold  for  optical 
experiments.  If  two  of  these  slices  similarly  situated,  as  in 
Fig.  307,  be  placed  between  the  eye  and  a  card  pierced  by  a 
hole,  the  hole  will  be  plainly  visible.  But  if  one  of  the  slices  be 

1  The  refractive  index  of  Canada  balsam  is  intermediate  between  the  indices  of  the 
crystal. 

2  Newton  came  to  the  conclusion  that  each  of  the  two  rays  had  two  sides  ;  and 
from  the  analogy  of  this  two-sidedness  with  the  two-endedness  of  a  magnet  the  term 
polarization  arose. 


POLARIZATION    OF    LIGHT. 


405 


FIG.  307. 


FIG.  308. 


slowly  rotated  in  a  plane  at  right  angles  with  the  beam  of 
light,  the  hole  will  grow  dimmer  until  the  slice  has  passed 
through  a  quarter  of  a  revolution  (as  represented  in  Fig.  308), 
when  it  disappears. 
If  the  rotation  be 
continued,  the  hole 
reappears,  faint 
first,  but  reaching  its 
maximum  brightness 
at  the  end  of  another  quarter-revolution.  Thus,  at  suc- 
cessive quarter-revolutions  it  is  alternately  extinguished  and 
restored. 

It  appears,  then,  that  light  which  has  passed  through  one 
trans-parent  slice  of  tourmaline  differs  so  much  from  common 
light,  that  a  second  similar  slice  may  act  like  an  opaque  body, 

and  stop  it  altogether. 
The  action  of  the  tour- 
maline may  be  com- 
pared to  that  of  a  grating 
(A,  Fig.  309)  formed  of 
parallel  vertical  rods, 
which  will  allow  all  vertical  planes  (as  a  a')  to  pass,  but  stops 
the  planes  (as  e  c')  that  are  at  right  angles  to  these  rods. 
Any  plane  that  has  succeeded  in  passing  one  grating  will 
readily  pass  a  second  similarly  placed.  But  if  the  second 
grating,  B,  be  turned  so  that  its  rods  are  at  right  angles  to 
the  first,  the  plane  that  has  succeeded  in  passing  through  the 
first  grating  will  be  stopped  by  the  second.  Light  in  this 
condition  is  polarized ;  polarization  is  either  the  act  of  pro- 
ducing the  change  in  the  light,  or  the  result  of  the  change, 
and  the  instrument  used  is  a  polarizer. 

In  order  to  understand  this  phenomenon,  it  is  necessary 
to  know  more  of  the  undulatory  theory  of  light.  This  theory 
supposes  that  the  undulations  in  ether  which  constitute  light 


FIG.  309. 


406 


ETHER    DYNAMICS. 


FIG.  310. 


are  much  like  undulations  in  a  cord  when  one  end  is  shaken 
by  a  hand1  as  seen  in  Fig.  310.    If  the  hand  move  vertically, 

all  the  undulations 
will  lie  in  a  vertical 
plane ;  if  the  move- 
ments of  the  hand  be 
horizontal  or  oblique, 
the  undulations  lie  in  corresponding  planes.  So  we  can 
produce  these  waves  on  the  rope  in  any  plane  passing 
through  the  rope,  and  can  change  rapidly  from  one  plane  to 
another.  These  waves  appear  differently  when  viewed  from 
different  sides.  It  is  believed  that  if  we  could  look  endwise 
at  a  ray  of  light  for  an  instant,  we  should  see  the  ether 
vibrations,  as  in  the  figure  of  the  rope,  in  one  plane ;  but  in 
only  a  thousandth  of  a  second  so  many  million  waves  reach  the 

/"»> 


FIG.  311. 

eye  that  there  is  time  for  the  vibrating  particles,  which,  like 
the  hand,  start  the  waves,  to  vibrate  in  many  planes.  In  an 
ordinary  beam  of  light,  as  it  reaches  the  eye,  there  are  there- 
fore undulations  in  all  possible  planes,  as  is  partially  repre- 
sented by  the  cross  section  A  (Fig.  311).  But  rectilinear 
motion  may  be  considered  as  the  resultant  of  two  similar 
motions  at  right  angles  to  each  other.  So  here,  for  many 
practical  purposes,  the  vibrations  may  be  regarded  as  taking 
place  in  only  two  sets  of  planes  at  right  angles  to  each  other, 

1  The  vibratory  motion  which  constitutes  light  must  be  transverse  to  the  direction 
of  the  ray  ;  it  cannot  be  in  the  direction  of  the  ray,  for  then  there  would  be  no  dif- 
ference between  the  different  sides  of  the  ray  ;  and  the  phenomena  of  polarization 
would  be  unexplainable  on  this  hypothesis. 


PLANE    OF    POLARIZATION.  407 

as  represented  by  B  of  the  same  figure.  Now,  when  a  ray  of 
light  consisting,  according  to  supposition,  of  undulations  in 
planes  at  right  angles  to  one  another  strikes  a  slice  of  tour- 
maline, its  molecular  structure  resolves  the  motion  into  two 
motions,  one  parallel  to,  and  the  other  perpendicular  to,  its 
axis.  The  former  of  these  is  transmitted  and  the  other 
is  absorbed.  By  this  means  fche  undulations  are  reduced  to 
those  in  parallel  planes  only,  as  represented  in  C.  The  un- 
aided eye  cannot  usually  detect  any  difference  between  com- 
mon and  polarized  light.  An  instrument  which  will  enable 
the  eye  to  detect  polarized  light  is  called  an  analyzer ;  thus 
the  first  slice  of  tourmaline  serves  as  a  polarizer,  and  the 
second  slice  as  an  analyzer.  A  complete  polarizing  apparatus, 
called  a  polariscope,  used  for  observing  the  phenomena  of 
polarized  light,  consists  essentially  of  a  polarizer  and  an 
analyzer. 

366.  Plane  of  polarization. 

There  are  several  ways  in  which  it  is  possible  to  restrict  the  vibra- 
tions of  a  ray  of  light  to  one  plane.  The  ray  in  such  a  case  is  said 
to  be  plane  polarized. 

It  will  be  shown  presently  that  light  is  partially  polarized  by 
ordinary  reflection.  The  plane  of  incidence  in  which  this  occurs  is 
called  the  plane  of  polarization.  It  is  still  an  open  question 
whether  the  vibrations  are  parallel  to  or  perpendicular  to  this 
plane,  the  evidence,  however,  being  decidedly  in  favor  of  the  latter 
view. 

With  a  uniaxial  doubly-refracting  crystal  (e.g.  Iceland  spar),  the 
ordinary  ray  is  polarized  in  a  plane  containing  the  incident  ray  and 
the  optic  axis. 

367.  Polariscope  consisting  of  two  Nicol  prisms. 

When  a  ray  of  light  becomes  split  by  double  refraction,  each  of 
the  resulting  rays  is  found  to  be  plane  polarized,  one  being  polarized 
in  the  plane  of  incidence,  the  other  at  right  angles  thereto. 

A  and  P  (Fig.  312)  represent  two  corks  having  Nicol  prisms  ex- 
tending through  them  lengthwise,  P  serving  as  a  polarizer,  and  A 


408 


ETHER    DYNAMICS. 


as  an  analyzer.  If  the  analyzer  A  be  turned  so  that  its  principal 
section  (see  §  363)  c'  df  R  is  parallel  to  the  principal  section  c  d  R  of 
the  polarizer  P,  the  ray  R  which  enters  P  as  unpolarized  light  be- 
comes polarized  and  the  extraordinary  ray  emerging  from  this 
prism  will  pass  freely  through  the  analyzer  A.  The  same  happens 


d' 


if  A  be  turned  through  an  angle  of  180°  so  as  to  bring  the  same 
planes  parallel  again.  But  if  A  be  adjusted  so  that  its  principal 
section  is  at  right  angles  to  that  of  the  polarizer  (as  in  the  lower  part 
of  Fig.  312),  then  the  ray  is  quenched  by  the  prism  A.  No  light 
leaves  the  analyzer,  and  accordingly,  to  an  eye  placed  at  the  end  of 
A,  the  field  of  vision  is  dark.  The  same  happens  if  A  be  turned 
through  an  angle  of  180°.  In  all  cases  where  the  principal  sections 
are  neither  parallel  nor  at  right  angles,  the  polarized  light  entering 
the  analyzer  is  separated  into  ordinary  and  extraordinary  rays,  and 
the  light  which  emerges  from  the  analyzer  varies  in  intensity  with 
the  angle  at  which  the  principal  sections  of  the  two  prisms  are  in- 
clined to  each  other. 

368.    Polarization  by  reflection. 

Malus  discovered  (1808),  while  looking  through  a  double-image 
prism  at  the  light  reflected  from  a  window  in  the  Luxembourg 
palace  in  Paris,  that  light  may  be  polarized  by  reflection. 

It  was  subsequently  found  that  the  amount  of  polarization  de- 
pends on  the  incident  angle.  The  angle  at  which  the  polarization 
is  a  maximum  is  called  the  angle  of  polarization  by  reflection,  which 
in  the  case  of  glass  is  between  55°  and  56°.  Then,  of  course,  if  a 


POLARIZATION    BY    REFRACTION. 


409 


Nicol  prism  be  held  in  certain  positions  the  reflected  light  will  pass 
through  it,  but  at  a  distance  of  90°  it  refuses  to  pass.  Again,  light 
which  has  been  polarized  by  reflection  from  one  glass  surface,  A 
(Fig.  313),  will  be  reflected  from  another  glass  surface,  B,  placed  so 


FTG   313. 

X 

that  the  plane  of  incidence  of  the  polarized  ray  is  parallel  to  the 
plane  of  polarization,  but  utterly  refuses  to  be  reflected  when  the 
plane  of  incidence  is  at  right  angles  to  the  plane  of  polarization, 
as  in  B'.  So  that  in  polariscopes  a  plate  (better  a  bundle  of  plates) 
of  glass  may  be  substituted  for  either  the  polarizer  or  the  analyzer. 
Light  reflected  obliquely  from  non-metallic  smooth  surfaces,  such 
as  water,  polished  furniture,  oil  paintings,  etc.,  is  found  on  examina- 
tion to  be  partially  polarized.  Sky-polarization  is  due  to  plane- 
polarization  effected  by  reflection  from  very  small  particles  of  water 
in  the  atmosphere. 

369.    Polarization  by  refraction. 

Not  only  the  reflected  portion  of  the  light  is  polarized,  but  also 
the  part  that  enters  the  medium  and  is  transmitted.  For  example, 
if  A  (Fig.  313)  be  a  transparent  glass  plate,  a  part  of  the  incident 
light  will  of  course  pass  through,  and  this  part  will  be  found  to  be 
partially  polarized,  but  in  a  plane  perpendicular  to  the  plane  of  in- 
cidence. Further,  Arago  found  that  the  reflected  beam  and  the 
transmitted  beam  contain  the  same  amount  of  polarized  light.  If 
the  transmitted  beam  be  examined  by  making  it  incident  upon  a 
second  transparent  surface,  it  will  be  reflected  only  if  the  plane  of 
incidence  is  made  parallel  to  the  plane  of  polarization  of  the  light. 


410  ETHER   DYNAMICS. 

370.  Circular  and  elliptical  polarization. 

In  all  polarization  thus  far  treated,  we  have  assumed  the  vibra- 
tions to  be  in  straight  lines  and  all  confined  to  one  plane.  It  can 
be  shown,  however,  that  if  two  such  waves,  one  a  quarter  of  a 
period  in  advance  of  the  other,  be  compounded,  with  their  planes 
perpendicular  to  each  other,  the  result  will  be  a  wave  in  which 
the  ether  particles  move  in  circles  or  ellipses,  according  as  the 
amplitudes  of  the  components  are  equal  or  not.  Such  a  wave  is 
circularly  or  elliptically  polarized,  and  since  (as  in  all  wave  motion) 
the  particles  move  successively,  the  wave  has  the  form  of  a  helix. 
For  fuller  discussion  of  this  form  of  polarization  and  the  methods  of 
producing  and  detecting  it,  the  student  is  referred  to  special  works 
on  light. 

371.  Chromatic  phenomena.1 

Take  the  simplest  case,  in  which  the  polarizer  and  analyzer  are 
sections  of  tourmaline  cut  parallel  to  the  axis.  (A  little  considera- 
tion will  show,  however,  that  the  explanation  holds  good  for  any 
other  form  of  analyzer  and  polarizer.)  P  (Fig.  314)  represents  the 
polarizer  and  A  the  analyzer.  P  .and  A  are  supposed  to  be  crossed. 
The  arrow  shows  the  direction  of  the  ray.  The  symbols  at  L,  B, 
C,  D,  are  intended  to  indicate  the  condition  of  the  light  in  those 
positions.  L  indicates  the  two  plane  component  waves  of  which 
ordinary  light  may  be  considered  as  composed.  One  of  these  is  the 
plane  of  the  paper,  the  other  a  plane  at  right  angles  to  it,  and  con- 
taining the  ray.  The  action  of  the  polarizer  P  is  to  remove  one  of 
these  components,  producing  at  B  a  plane-polarized  wave  whose 
plane  coincides  with  the  plane  of  the  paper.  This  wave,  lying  in  a 
plane  at  right  angles  to  those  waves  which  the  analyzer,  when  in 
the  position  supposed,  will  allow  to  pass,  is  cut  off,  and  a  dark  field 

results.    Any  wave  not  parallel 
to  the  plane  of    B  would  evi- 
dently pass  through  A,  either 
•=.  wholly  or  in  part.       Suppose 
now  any  doubly-refracting  sub- 
s  A  stance,  as  a  crystalline  film  S, 

Pm  314  to  be  placed  between  P  and  A. 

The  plane-polarized  ray  B,  ex- 
cept in  certain  special  cases,  is  doubly  refracted  and  separated  into 

1  In  the  explanation  of  these  phenomena  we  have  adopted  largely  the  language  of 
Prof.  Cross  of  the  Mass.  Inst.  of  Technology. 


B 


CHROMATIC    PHENOMENA.  411 

two  component  plane-polarized  rays,  indicated  by  C,  with  their 
planes  of  vibration  at  right  angles  to  each  other,  and  inclined  to  the 
original  plane  of  .vibration  of  B.  These  rays  at  C,  in  which  the 
vibrations  are  not  parallel  to  B,  and  hence  not  at  right  angles  to  the 
axis  of  the  tourmaline  section  A,  are  not  wholly  cut  off,  but,  as  A 
is  a  doubly-refracting  crystal,  are  again  each  separated  into  two 
sets  of  rays  ;  one  set  of  these  having  its  plane  of  vibration  at  right 
angles  to  B  and  hence  parallel  to  the  axis  of  A,  is  allowed  to  pass 
as  indicated  by  D,  while  the  other  set  is  cut  off.  This  explains  the 
illumination  of  the  field. 

' '  The  light  transmitted  under  these  circumstances  is  generally 
colored,  for  the  following  reason  :  In  traversing  the  doubly-refract- 
ing crystal  S,  the  components  into  which  B  is  separated  travel  with 
different  velocities.  Hence  one  of  these  components  gains  on  the 
other  by  an  amount  which,  other  things  being  equal,  depends  on 
the  thickness  of  S.  Suppose  the  gain  to  be  such  that  on  emerging 
from  S  one  of  the  components  of  C  is  in  advance  of  the  other  by 
one  wave-length  of  red  light,  as  shown  at  O  O'  (Fig.  315).  Assuming 
a  tourmaline  section  or  equivalent  analyzer  to  be  used,  one  compo- 
nent only  of  each  pair  into  which  O  and  O'  are  resolved  passes  through 
A,  and  these  components  (e  e'.  Fig.  315)  are  in  opposite  phases,  and 
hence  interfere.  The  components  o  o'  are  not  transmitted  by  the 
analyzer.  The  red  rays  are  therefore  struck  out  from  the  white 
light  of  the  original  beam,  and  the  field  appears  of  a  greenish  color. 
Evidently,  if  the  thickness  of  S  (Fig.  314)  be  such  that  one  system 
gains  upon  the  other  an  amount 
equal  to  any  whole  number  of  wave- 
lengths or  even  number  of  half 
wave-lengths  of  light  of  any  parti- 
cular color,  that  color  will  disappear 
from  the  transmitted  rays  at  D.  If  Q\/Q 
the  gain  be  equal  to  any  odd  number 
of  half  wave-lengths,  the  compo- 
nents emerging  from  the  analyzer 
will  have  the  same  phase,  and  that  | 

color  will  be  present  in  the  trans-  A 

mittedbeam.i 

"If  a  crystal  of  Iceland  spar  be  substituted  for  the  tourmaline 
analyzer  A,  both  systems  of  rays,  D  (Fig.  314)  and  the  set  at  right 

1  Read  in  connection  with  the  last  two  statements  Glazebrook's  Physical  Optics, 
p.  374 ;  also  Lloyd's  Undulatory  Theory  of  Light,  pp.  219,  220. 


412 


ETHER    DYNAMICS. 


angles  to  D,  will  be  transmitted.  In  this  case  the  colors  of  the  two 
sets  of  transmitted  rays  are  always  complementary  ;  that  is,  if  one 
be  red,  the  other  is  green  ;  if  one  be  blue,  the  other  is  yellow,  etc. 
This  is  evident  from  an  examination  of  the  component  plane-waves 
issuing  from  the  doubly-refracting  crystal  of  Iceland  spar  at  A 
(Fig.  315).  It  will  be  seen  that  when  those  of  one  set  meet  crest 
to  trough,  those  of  the  other  set  will  meet  crest  to  crest.  Hence 
any  color  struck  out  in  one  set  will  predominate  in  the  other  ;  that 
is,  the  colors  of  the  two  sets  must  be  complementary.  Rotating  the 
analyzer  through  90°  changes  each  color  to  the  complementary 
hue." 

372.    Description  of  a  simple  polariscope. 

D  (Fig.  316)  is  a  plate  of  glass  about  15  cm  square,  used  as  a 

polarizer.  A  is  the  ana- 
lyzer,  —  preferably  a  Nicol 
prism,  —  so  placed  as  to 
view  the  center  of  the  glass 
at  the  proper  polarizing 
angle  (about  55°).  The 
prism,  mounted  in  a  cork, 
should  be  free  to  rotate  in 
its  support.  S  is  a  piece  of 
ground  glass  used  to  cut  off 
the  images  of  outside  ob- 
jects. G  is  a  glass  shelf,  on  which  objects  to  be  examined  are 
placed.  The  instrument,  covered  with  a  black  cloth,  is  placed  on  a 
table  with  S  toward  a  window. 

Experiment  2.  —  Place  on  the  support  G  a  thin  film  of  selenite  or  mica, 
and  slowly  rotate  the  analyzer.'  A  beautiful  display  of  colors  will  appear. 
At  a  certain  point  they  will  appear  of  maximum  brilliancy,  then  they 
will  gradually  fade  away  and  change  into  their  complementaries.  (See 
§371.) 


FIG.  316. 


37.3.    Ring-system  of  plates  perpendicular  to 


A  different  class  of  appearances  is  presented  when  a  plate  of  any 
uniaxial  crystal  is  examined  in  a  convergent  or  divergent  pencil  of 
plane-polarized  light.  Since  the  rays  are  oblique,  the  thickness  of 
the  plate  traversed  increases  with  the  angle  of  incidence,  being  least 
for  a  ray  parallel  to  the  axis  and  normal  to  the  plate.  In  this  case 


RING-SYSTEM   OF   PLATES. 


413 


the  ray  passes  through  the  plate  parallel  to  the  optic  axis,  and  is 
not  doubly  refracted.  Let  E  be  the  position  of  the  eye  immediately 
behind  the  analyzer  (not  shown 
in  Fig.  317),  S  S'  the  plate,  and 
OE  the  direction  of  the  axis. 
Now  an  oblique  ray  that  reaches 
the  eye  from  any  point  P  has 
been  doubly  refracted  in  passing 
through  the  plate,  P  a  and  P  6 
representing  the  component  mo- 
tions. As  the  speeds  of  the 
component  rays  are  not  equal, 
a  retardation  which  is  greater 
as  P  is  farther  from  0  will  occur 
in  the  case  of  one  of  these. 

In  general,  the  analyzer  again 
subdivides  the  rays  P  a  and  P  6 


IT 

FIG.  317. 


into  two  mutually  perpendicu- 
lar sets,  one  component  only  of  each  set  being  transmitted.  These 
latter  interfere  more  or  less  destructively  according  to  the  retarda- 
tion that  has  been  suffered  by  one  of  them,  the  interference  being 
complete  for  any  color  when  the  difference  of  phase  is  half  a  wave- 
length for  this  color.  It  is  clear,  then,  that  the  field  will  be 
occupied  by  a  series  of  concentric  rings  spectral  colored  from 
the  center  outward,  the  appearance  being  similar  to  that  of 
Newton's  rings. 

Let  us  now  consider  two  planes  through  0  E,  one  parallel  to  the 
plane  of  primitive  polarization  and  the  other  perpendicular  to  it. 
Let  their  traces  on  S  S'  be  M  M'  and  N  N'.  Now  all  rays  travers- 
ing the  plate  in  these  planes  will  be  unaffected,  since  the  principal 
section  of  the  crystal  in  the  one  case  coincides  with  the  plane  of 
polarization  of  the  incident  signs,  and  in  the  other  case  is  perpen- 
dicular to  it. 

These  rays,  therefore,  will  or  will  not  be  transmitted  by  the 
analyzer  according  as  its  principal  section  is  parallel  to  or  perpen- 
dicular to  the  primitive  plane  of  polarization.  In  the  former  case 
we  shall  have  a  white  cross  over  the  ring  system,  in  the  latter  a 
dark  one. 

A  and  B  (Fig.  818)  illustrate  these  phenomena  only  in  a  very 
imperfect  way,  since  the  coloring  of  the  figures  is  necessarily 
absent. 


414 


ETHER    DYNAMICS. 


374.    Rotatory  polarization. 

It  was  observed  by  Arago  in  1811  that  if  plane  polarized  light  be 
transmitted  by  a  plate  of  quartz  cut  perpendicular  to  the  axis,  the 

plane  of  polarization  is  rotated 
through  a  certain  angle.  The 
investigations  of  Biot  showed 
this  angle  to  be  proportional  to 
the  thickness  of  the  plate  and 
approximately  to  the  inverse 
square  of  the  wave-length. 
For  example,  if  such  a  plate  of 
quartz  be  placed  between  two 
crossed  nicols,  the  dark  field 
immediately  becomes  bright, 
arid  also  colored,  if  the  light 
employed  be  not  homogeneous. 
That  is,  the  plate  has  turned 
the  plane  of  polarization  of  the 
light,  so  that  when  it  is  inci- 
dent upon  the  analyzer  there 
is  a  component  of  the  vibration 
which  is  parallel  to  the  princi- 
pal section,  and  so  can  be  trans- 
mitted. As  the  different  colors 
are  rotated  through  different 
angles,  the  transmitted  compo- 
nents are  not  mixed  in  the 
same  proportions  as  in  the  in- 
cident light,  and  so  the  field  is 
colored,  the  particular  color 
depending  on  the  position  of 
the  analyzer.  It  was  found  that  some  specimens  of  quartz  cause 
rotation  to  the  right  (i.e.  clockwise),  and  so  are  called  dextrogyrate, 
while  others  cause  rotation  to  the  left,  and  are  called  levogyrate. 

Many  other  substances,  including  some  liquids  and  solutions, 
also  possess  this  property,  though  to  a  much  less  degree.  Thus, 
while  a  plate  of  quartz  1  mm  thick  rotates  the  plane  of  red  light 
nearly  18°,  the  same  thickness  of  turpentine  produces  a  rotation  of 
only  a  quarter  of  a  degree. 

The  method  of  determining  this  angle  is  extremely  simple.  So- 
dium light  is  commonly  used,  and  the  polarizer  and  analyzer  are 


FIG.  318. 


THE    SACCHARIMETER.  415 

so  adjusted  that  the  field  is  dark.  The  substance  to  be  examined 
is  then  inserted  between  them,  and  the  analyzer  is  turned. till  the 
field  is  again  dark ;  the  angle  thus  turned  through  is  the  rotation 
produced  by  the  substance.  Liquids  and  vapors  are  studied  by 
enclosing  them  in  a  tube  of  known  length  through  which  the  polar- 
ized light  is  passed. 

These  phenomena  are  explained  by  supposing  that  when  a  beam 
of  plane  polarized  light  is  incident  upon  the  quartz  plate  it  is 
doubly  refracted,  or  divided,  not  into  two  plane-polarized  beams, 
but  into  two  circularly-polarized  beams,  the  directions  of  motion 
being  opposite.  If  now  these  traverse  the  crystal  with  slightly 
different  speeds,  it  is  clear  that  when,  on  emerging,  they  are  com- 
pounded, the  resultant  plane  of  motion  and  hence  plane  of  polari- 
zation will  not  be  parallel  to  that  of  the  incident  light.  Evidently 
it  will  have  been  turned  through  an  angle  depending  on  the  thick- 
ness of  the  crystal  and  on  the  difference  of  speeds  of  the  two  beams 
in  it. 

In  Fig.  319  is  shown  the  tourmaline  tongs,  a  simple  form  of  po- 
lariscope.  Two  plates  of  tourmaline,  cut  as  described  in  §  365, 
are  mounted  so  as  to  turn  in  eyes  formed  at  the  extremities  of  the 
looped -wire.  If  the  plates  be  so  arranged  that  the  light  is  com- 


FlG.  319. 

pletely  extinguished,  and  a  pebble  (quartz)  spectacle  lens  be  placed 
between  the  tourmalines  thus  arranged,  the  light  will  again  pass, 
showing  the  effects  of  rotation  of  the  plane  of  polarization.  This 
is  accepted  as  a  test  of  the  genuineness  of  quartz  lenses. 

375.    The  saccharimeter. 

The  angle  of  rotation  of  a  saccharine  solution  varies  with  the 
number  of  grams  of  sugar  in  a  cubic  centimeter  of  the  solution. 
On  this  principle  is  constructed  a  polariscope,  called  a  saccharlmeter, 
which  is  used  for  the  express  purpose  of  determining  the  percentage 


416  ETHER    DYNAMICS. 

of  pure  sugar  in  an  aqueous  solution,  and  hence  the  commercial 
value  of  a  syrup.  This  instrument  is  furnished  with  a  scale  em- 
pirically graduated  so  that  the  percentage  can  be  read  directly,  or 
easily  calculated. 

SECTION   XII. 

THERMAL    EFFECTS    OF    RADIATION. 

376.  Heat  not  transmitted  by  radiation.  —  We  have  learned 
that  heat  may  travel  through  matter   (by  conduction),  and 
with  matter  (by  convection),  and  it  is  sometimes  stated  that 
there  is  a  third  method  by  which  it  travels,  viz.  "  radiation." 
Heat  itself  is  not  transferred  by  radiation  at  all ;  heat  gen- 
erates radiation  (i.e.  ether  waves)  at  one  place,  and  radiation 
produces  heat  at  another;  it  is  radiation  which  travels,  not 
heat.     It  does  not  exist  as  heat  in  the  intervening  space,  and 
therefore  does  not  necessarily  heat  the  substance  filling  that 
space.     Heat  can  flow  only  one  way,  viz.  from  a  given  point  to 
a  point  that  is  colder ;  radiation  travels  in  all  directions.     The 
sun  sends  us  no  heat,  but  it  sends  radiations  which  the  earth 
transforms  into  heat ;  but  it  should  be  borne  in  mind  that 
while  it  is  radiation  it  is  not  heat,  and  vice  versa.     Tempera- 
ture is  a  condition  of  bodies,  not  of  radiations  ;  wave-lengths 
belong  to  radiations,  not  to  heat  which  produces  them. 

377.  Diathermancy  and  athermancy.  —  What  becomes   of 
radiations    which   strike    a   body  depends   largely  upon  the 
character  of  the  body.     If  the  nature  of  the  body  be  such 
that  its  molecules  can  accept  the  motion  of  the  ether,  the 
vibrations  of  ether  are  said  to  be  absorbed  by  the  body  and 
the  body  is  thereby  heated,  i.e.  the  undulations  of  ether  are 
transformed  into  molecular  energy  or  heat.      Glass,  for  in- 
stance, allows  the  sun's  radiations  to  pass  very  freely  through 
it,  and  very  little  is  transformed  into  heat.     But  if  the  glass 
be  covered  with  the   soot  of  a  candle  flame,  the  soot  will 


DIATHERMANCY    AND    ATHERMANCY.  417 

absorb  the  radiations  and  the  glass  become  heated.  Observe 
how  cold  window-glass  may  remain,  while  radiations  pour 
through  it  and  heat  objects  in  the  room.  Only  those  radia- 
tions that  a  body  absorbs  heat  it ;  those  that  pass  through  it  do 
not  affect  its  temperature. 

Bodies  that  transmit  radiations  freely  are  said  to  be  dia- 
thermanous, while  those  that  absorb  them  largely  are  called 
athermanous.  These  terms  bear  the  same  relation  to  the 
transmission  of  radiant  energy  of  any  and  all  wave-lengths  as 
do  transparency  and  opacity  to  the  transmission  of  light  or 
visible  radiations.  The  most  diathermanous  substance  known 
is  rock  salt.  A  solution  of  iodine  in  carbon  bisulphide 
absorbs  almost  completely  the  rays  of  the  visible  spectrum, 
but  transmits  almost  completely  all  of  longer  wave-length 
than  the  red  end  of  the  spectrum.  A  plate  of  alum  acts  in 
the  reverse  manner,  transmitting  the  visible  and  absorbing 
the  invisible.  Among  liquids  carbon  bisulphide  is  exception- 
ally transparent  to  all  forms  of  radiation  ;  while  water,  trans- 
parent to  short  waves,  absorbs  the  longer  waves,  and  is  thus 
quite  athermanous. 

Experiment  1.  —  Bring  the  bulb  of  an  air  thermometer  into  the  focus 
of  a  burning-glass  exposed  to  the  sun's  rays.  The  radiation  concentrated 
on  the  enclosed  air  scarcely  affects  this  delicate  instrument. 

Experiment  2.  —  Cover  the  outside  of  the  bulb  of  the  air  thermometer 
with  lamp-black  and  repeat  the  last  experiment.  The  lamp-black 
absorbs  the  radiant  energy,  and  the  heat  conducted  through  the  glass  to 
the  enclosed  air  raises  its  temperature  and  causes  it  to  expand  and 
rapidly  push  the  liquid  out  of  the  stem. 

Dry  air  is  almost  perfectly  diathermanous.  All  of  the 
sun's  radiations  that  reach  the  earth  pass  through  the  atmos- 
phere, which  contains  a  vast  amount  of  aqueous  vapor.  This 
vapor,  like  water,  is  comparatively  opaque  to  long  waves  ; 
hence  it  modifies  very  much  the  character  of  the  radiations 
which  reach  the  earth.  This  fact,  together  with  what  we  have 


418  ETHEK    DYNAMICS. 

learned  from  Exp.  1,  enables  us  to  understand  the  method  by 
which  our  atmosphere  becomes  heated.  First,  that  portion 
of  the  radiant  energy  which  comes  to  us  from  the  sun  in  the 
form  of  relatively  long  waves  is  stopped  by  the  watery  vapor 
in  the  air,  which  is  thereby  heated.  The  portion  that  comes  to 
us  in  short  waves  escaping  this  absorption  heats  the  earth  by 
falling  upon  it.  The  warmed  earth  loses  its  heat,  —  partly  by 
conduction  to  the  air,  still  more  largely  by  radiation  out- 
ward. The  form  of  radiation,  however,  has  been  greatly 
changed;  for  now,  coming  from  a  body  at  a  low  temperature, 
it  is  chiefly  in  long  waves  that  the  energy  is  transmitted  ; 
while,  as  we  have  seen,  it  was  largely  in  the  form  of  short 
waves  that  the  earth  received  its  heat.  But  it  is  exactly 
these  long  waves  which  are  most  readily  stopped  by  the  atmos- 
phere ;  hence,  the  atmosphere,  or  rather  the  aqueous  vapor 
of  the  atmosphere,  acts  as  a  sort  of  trap  for  the  energy  which 
comes  to  us  from  the  sun. 

Remove  the  watery  vapor  (which  serves  as  a  "  blanket "  to 
the  earth)  from  our  atmosphere,  and  the  chill 
resulting  from  the  rapid  escape  of  heat  by 
radiation  would  probably  put  an  end  to  all 
animal  and  vegetable  life.  Glass  does  not 
screen  us  from  the  sun's-  heat,  but  it  can  very 
effectually  screen  us  from  the  heat  radiated 
from  a  stove  or  any  other  terrestrial  object. 
Glass  is  diathermanous  to  the  sun's  radiations 
(simply  because  they  have  already  lost  most 
of  the  very  long  waves  by  atmospheric  ab- 
sorption), but  quite  athermanous  to  other 
radiations.  This  is  well  illustrated  in  the 
case  of  hot-beds  and  green-houses.  The 
sun's  rays  pass  through  the  glass  of  these 
enclosures  almost  unobstructed,  and  heat  the 
FIG.  320.  earth  ;  but  the  radiations  given  out  in  turn 


THE    RADIOMETER.  419 

by  the  earth  are  such  as  cannot  pass   out  through  the  glass, 
and  hence  the  heat  is  retained  within  the  enclosures. 

378.     The  radiometer. 

Fig.  320  represents  an  instrument  called  a  radiometer.  The 
moving  part  is  a  small  vane  resting  on  the  point  of  a  needle.  It  is 
so  nicely  poised  on  this  pivot  that  it  rotates  with  the  greatest  free- 
dom. To  the  extremities  of  each  of  the  four  arms  of  the  vane  are 
attached  disks  of  aluminum  or  mica  which  are  light  on  one  side 
and  black  on  the  other.  The  whole  is  enclosed  in  a  glass  bulb  from 
which  the  air  is  nearly  exhausted.1 

Exposed  to  the  radiations  of  the  sun,  a  candle  flame,  or  even  the 
radiations  from  the  human  body,  the  vane  will  rotate  with  the  un- 
blackened  faces  in  advance.  The  blackened  faces  absorb  the 
radiant  energy  and  become  heated,  the  air  particles  remaining  in  the 
bulb  by  striking  against  them  have  their  speed  increased,  and  thus 
results  an  increased  pressure  upon  the  blackened  surfaces,  causing 
a  more  or  less  rapid  revolution  of  the  arms. 

It  can  be  shown  that  the  glass  bulb  tends  to  rotate  in  the  oppo- 
site direction  to  that  of  the  vane.  This  is  a  proof  that  the  rotation 
is  due  to  action  and  reaction  between  the  vane  and  the  glass,  and 
not,  as  it  might  appear,  between  the  vane  and  the  source  of  radia- 
tion. The  radiometer  thus  serves  indirectly  to  transform  radiant 
energy  into  mechanical  work,  and  may  be  used  to  measure  the 
mechanical  effects  of  radiant  energy.  For  example,  the  radiations 
from  two  candle  flames  produce  twice  the  effect  of  that  from  one  ; 
and  when  the  distance  from  the  source  of  radiations  is  doubled  the 
effect  is  one-fourth  as  great.  Hence  the  radiometer  may  be  used 
to  verify  in  a  very  direct  and  simple  manner  the  law  of  inverse 
squares  as  applied  to  radiant  energy.  It  is  also  used  in  a  variety 
of  experiments  to  illustrate  the  mechanical  effects  of  the  rapidly 
moving  molecules  of  gases. 

If  the  opening  at  the  top  be  kept  open  and  connected  with  a 
pump,  so  that  the  exhaustion  can  be  regulated  at  will,  then  after 
a  certain  degree  of  exhaustion  has  been  attained  the  black  disks 
exposed  to  radiation  are  repelled  and  rotation  ensues.  If  the 

1  The  bulb  must  be  exhausted  of  air  till  the  mean  free  path  of  the  air  particles  is 
greater  than  the  distance  of  the  glass  from  the  surface  of  the  vane,  so  that  particles 
after  impinging  on  the  disks  do  not  as  a  rule  collide  with  other  particles  before 
reaching  the  glass. 


420 


ETHER    DYNAMICS. 


exhaustion  be  gradually  increased,  a  maximum  speed  is  reached ; 
further  exhaustion  diminishes  the  speed,  and  ultimately  rotation 


379.    Solar  radiation.     Pyrheliometer. 

Fig.  321  represents  an  instrument,  called  a  pyrheliometer,  used 
to  determine  solar  radiation.  It  consists  of  a  shallow  cylindrical 
vessel,  A,  of  thin  metal.  The  upper  surface  is  covered  with  lamp 
black.  The  bulb  of  a  thermometer  is 
enclosed  in  this  cylinder  and  its  stem  in 
a  tube,  B  ;  the  remaining  space  in  cylin- 
der and  tube  is  filled  with  water.  The 
blackened  surface  is  turned  toward  the 
sun,  and  to  ensure  that  the  rays  are 
normal  to  this  surface  the  shadow  of  the 
cylinder  is  made  to  cover  exactly  and 
coincide  with  the  disk  C. 

First  the  instrument,  sheltered  from 
the  sun,  is  permitted  to  radiate  its  heat 
into  the  clear  sky  for  (say)  five  minutes. 
Let  the  fall  in  temperature  be  r°. 

Next  it  is  turned  to  the  sun  for  five 
minutes.  Let  the  rise  in  temperature  be 


Fio.  321. 


Finally  it  is  allowed  (at  its  increased 
temperature)  to  radiate  into  the  clear  sky 
as  before  for  five  minutes.     Let  the  fall  of  temperature  be  r'0. 

Now  since  r  denotes  the  change  of  temperature  during  radiation 
into  clear  sky  before  heating,  and  r'  the  same  after  heating,  the 
change  of  temperature  during  the  heating,  due  to  radiation,  con- 

r-f-  r' 
duction,  etc.,  will  be  very  nearly  a  mean  between  the  two,  or  — — •  ; 

but  it  is  evident  that  this  cooling  effect  takes  place  even  when  the 
instrument  is  receiving  the  sun's  radiations,  and  tends  to  diminish 
the  heating  effect  produced  by  these  radiations.  Hence,  therefore, 
the  whole  heating  effect  will  be 


This  is  the  number  of  degrees  which  the  sun's  radiant  energy  is 
able  to  raise  the  temperature  of  n  kilograms  of  water  (suitable  al- 


ALL    BODIES    RADIATE    HEAT.  421 

lowance  being  made  for  the  water  equivalent  of  the  vessel  and 
thermometer)  when  it  falls  upon  a  units  of  area  of  lamp  black  for 
m  units  of  time.  Then  the  radiant  energy  received  per  unit  area 
during  one  unit  of  time  is  equivalent  to 


calories  of  heat.     By  Joule's  equivalent  we  are  able  to  calculate  the 
energy  in  mechanical  units. 

It  is  estimated  that  if  the  whole  radiation  received  by  the  earth 
from  the  sun  were  employed  in  melting  ice,  it  would  in  a  year  melt 
a  layer  of  ice  all  round  the  earth  137  feet  in  thickness  (Young).1 
Only  a  very  small  fraction  of  the  sun's  radiations  are  intercepted 
by  the  earth.  Lord  Kelvin  estimates  that  the  total  energy  emitted 
by  the  sun  is  at  the  rate  of  7000  horse-power  per  square  foot  of 
radiating  surface. 

380.  All  bodies  radiate  heat.  — Hot  bodies  usually  part  with 
their  heat  much  more  rapidly  by  radiation  than  by  all  other 
processes  combined.      But  cold  bodies,  like  ice,  emit  radia- 
tions even  when  surrounded  by  warm  bodies.     This  must  be 
so  from  the  nature  of  the  case,  for  the  molecules  of  the  coldest 
bodies  possess  some  motion,  and  being  surrounded  by  ether 
they  cannot  move  without  imparting  some  of  their  motion  to 
the  ether,  and  to  that  extent  becoming  themselves  colder. 

381.  Prevost's  theory  of  exchanges.  —  Let  us  suppose  that 
we  have  two  bodies,  A  and  B,  at  different  temperatures,  —  A 
warmer  than  B.     Radiation  takes  place  not  only  from  A  to  B, 
but  from  B  to  A ;  but,  in  consequence  of  A's  excess  of  tem- 
perature, more  radiation  passes  from  A  to  B  than  from  B  to 
A,  and  this  continues   until  both  bodies   acquire  the  same 
temperature.     At  this  point  radiation  by  no  means   ceases, 
but  each  now  gives  as  much  as  it  receives,  and  thus  equilib- 
rium is  kept  up.      This  is  known  as  "Prevost's  Theory  of 
Exchanges." 

1  For  further  information  concerning  solar  radiation,  see  Young's  Elements  of 
Astronomy,  pp.  147-153. 


422  ETHER    DYNAMICS. 

382.  Good  absorbers,  good  radiators. 

Experiment  3.  — Select  two  small  tin  boxes  of  equal  capacity,  — one 
should  be  bright  outside,  while  the  other  should  be  covered  thinly  with 
soot  from  a  candle  flame.  Cut  a  hole  in  the  cover  of  each  box  large 
enough  to  admit  the  bulb  of  a  thermometer.  Fill  both  boxes  with  hot 
water,  and  introduce  into  each  a  thermometer.  They  will  register  the 
same  temperature  at  first.  Set  both  in  a  cool  place,  and  in  half  an  hour 
you  will  find  that  the  thermometer  in  the  blackened  box  registers  several 
degrees  lower  than  the  other.  Then  fill  both  with  cold  water,  and  set 
them  in  front  of  a  fire  or  in  the  sunshine,  and  it  will  be  found  that  the 
temperature  in  the  blackened  box  rises  more  rapidly. 

As  bodies  differ  widely  in  their  absorbing  power,  so  they 
do  in  their  radiating  power,  and  it  is  found  to  be  universally 
true  that  good  absorbers  are  good  radiators,  and  bad  absorbers 
are  bad  radiators.  Much,  in  both  cases,  depends  upon  the 
character  of  the  surface  as  well  as  of  the  substance.  Bright, 
polished  surfaces  are  poor  absorbers  and  poor  radiators ; 
while  tarnished,  dark,  and  roughened  surfaces  absorb  and 
radiate  rapidly.  Dark  clothing  absorbs  and  radiates  more 
rapidly  than  light  clothing. 

383.  Dew.  • —  It  requires  no  elaborate  experiments  to  show 
that   some  bodies    radiate  more    rapidly  than   others.      All 
nature  testifies  to  this,  every  still,  cloudless  summer  night. 
During  the  day  objects  on  the  earth's  surface  gain  more  heat 
by  radiation,  than  they  lose,  but  as  soon  as  the  sun  has  set 
this  is  reversed.     Then  everything  begins  to  cool  by  radia- 
tion into  space.     Objects  becoming  cool,  the  air  in  contact 
with  them  becomes  chilled;  its  watery  vapor  condenses,  and 
collects  in  tiny  liquid  drops   on  their  surfaces.     But  these 
dew-drops  collect  much  more  abundantly  on  certain  things, 
such  as  grasses  and  leaves,  than  on  others,  such  as  stones  and 
earth.     The  reason  that  dew  does  not  collect  on  the  latter  so 
freely,  is  because  of  their  poor  radiating  power ;  they  do  not 
get  cool  as  rapidly. 


QUESTIONS.  423 


Questions. 

1.  What  objections  can  you  raise  to  the  term  "  radiant  heat "  ? 

2.  Explain  why  the  temperature  of  a  hotbed  is  above  that  of  the  sur- 
rounding air. 

3.  How  could  you  separate  the  dark  radiation  of  an  electric  arc  lamp 
from  the  luminous  radiation  ? 

4.  How  can  you  demonstrate  the  existence  of  ether  waves  of  greater 
length  than  the  light-giving  waves  ? 

5.  Ice  appears  to  radiate  cold.     Explain  the  phenomenon  by  Provost's 
theory. 

6.  A  radiometer  placed  near  ice  rotates  with  the  blackened  sides  of  its 
disks  in  advance.     Explain. 

7.  What  parts  of  the  spectrum  are  invisible  to  the  eye  ? 

8.  How  can  you  prove  the  existence  of  invisible  solar  rays  ? 

9.  On  what  does  the  color  of  bodies  primarily  depend? 

10.  What  agency  does  a  body  perform  in  determining  its  own  color 
when  illuminated  with  white  light  ? 

11.  a.  Why  is  grass  green?    b.  Snow,  white?    c.  Soot,  black? 

12.  How  does  a  spectrum  produced  by  a  crown  glass  prism  differ  from 
a  spectrum  produced  by  a  flint  glass  prism  ? 

13.  State  some  phenomenon   which  the  undulatory  theory  alone  is 
competent  to  explain. 

14.  Describe  the  appearance  which  an  iridescent  soap  bubble  would 
present  in  a  monochromatic  light. 

15.  Objects  seen  across  the  top  of  a   hot  stove  appear  unsteady  and 
indistinct.     Explain. 

16.  State  how  with  a  pair  of  tourmaline  tongs  you  may  distinguish  a 
glass  spectacle  lens  from  a  quartz  lens. 

17.  State  how  the  sensation  of  purple  is  produced. 

18.  What  is  meant  by  the  artist's  three  primary  pigments  ? 

19.  Describe  the  surface  which  a  hot-water  vessel  should  have  in  order 
to  retain  its  heat  well. 

20.  Suppose  beams  of  sunlight  enter  a  dark   room  through  two  aper- 
tures in  a  shutter,  and  a  blue  glass  be  placed  in  the  path  of  one  beam 
and  a  yellow  glass  in  the  path. of  the  other,     a.  What  color  will  that 
portion  of  a  white  wall  appear  where  the  two  images  of  the  sun  over- 
lap ?    6.  State  the  result  if  one  of  the  apertures  be  closed  and  the  beam 
from  the  other  aperture  be  made  to  pass  through  both  colored  glasses. 

21.  When  red  and  green  sensations  coexist  what  is  the  resulting  sen- 
sation ? 


424 


ETHER    DYNAMICS. 


22.  What  phenomenon  shows  that  ether-waves  do  not  traverse   all 
substances  with  equal  speed  ? 

23.  State  how  light  may  "turn  a  corner." 

24.  What  utility  is  there  in  keeping  certain  parts  of  a  steam  engine 
very  bright? 


SECTION  XIII. 

SOME    OPTICAL    INSTRUMENTS. 

384.  Compound  microscope.  —  When  it  is  desired  to  magnify 
an  object  more  than  can  be  done  conveniently  and  with 
distinctness  by  a  single  lens,  two  convex  lenses  are  used, — 
one,  0  (Fig.  322),  called  the  objective,  to  form  a  magnified 
real  image  a'  b'  of  the  object  a  b  ;  and  the  other,  E,  called  the 
eye-piece,  to  magnify  this  image  so  that  the  image  a'  b'  appears 
of  the  size  a"  b"  .  Instead  of  looking  at  the  object  as  when 
we  use  a  simple  lens,  we  look  at  the  real  inverted  image,  a'b', 
of  the  object. 

This      represents       the     simplest 
b"          possible  form  of  the  compound  micro- 
scope.     In    practice,     however,    the 
construction  is  more  complicated. 

Fig.  323  represents  a  perspective 
and  a  sectional  view  of  a  simple  form 
of  a  modern  compound  microscope. 
The  body  of  the  instrument  consists 
of  a  series  of  brass  tubes  movable  one 
within  another.  In  the  upper  end  H 
is  the  ocular  or  eye  piece.  It  consists 
of  two  plano-convex  lenses  o  and  n, 
the  former  called  the  eye-lens,  the 
latter  called  the  field  lens.  The  ad- 
vantages derived  from  the  use  of  two  lenses  in  the  eye-piece 
are  as  follows: 

1.  The  combination  diminishes  spherical  aberration  and  thereby 
increases  the  flatness  of  the  field.  The  images  a'  6'  and  a"  b"  (Fig.  323) 
are  in  reality  curved  in  consequence  of  the  spherical  aberration 


FIG.  322. 


COMPOUND    MICROSCOPE. 


425 


caused  by  the  objective.     The  effect  of  the  field  lens  is  to  correct 
this  curvature  in  a  measure. 

2.  The  combination  increases  the  field  of  view,  so  that  a  larger 
area  of  the  object  is  made  visible  at  the  same  view. 

3.  The  combination  diminishes  chromatic  aberration. 

All  microscopes,  however,  should  be  furnished  with  an  achro- 


FlG.  323. 


matic  objective.  This  consists  of  two  to  four  achromatic  lenses, 
(the  achromatic  triplet,  the  most  common  form,  is  represented  on 
an  enlarged  scale  at  L  in  Fig.  323),  combined  so  as  to  act  as  a 
single  lens  of  short  focus.  By  the  use  of  several  lenses,  the  aber- 
rations can  be  better  corrected  than  with  a  single  lens. 


426 


ETHER    DYNAMICS. 


The  object  to  be  examined  is  placed  on  a  stage,  S,  and,  if 
the  object  be  transparent,  it  is  strongly  illuminated  by  focus- 
ing light  upon  it  by  means  of  a  concave  mirror,  M.  If  the 
object  be  opaque,  it  is  illuminated  by  light  directed  upon  it 
obliquely  from  above  by  the  converging  lens  N. 

385.    Oculars. 

The  negative  (or  Huyghenian)  ocular  consists  of  two  convex 
lenses  of  crown  glass,  F  and  E  (Fig.  324),  the  convex  surfaces 
being  turned  toward  the  object  glass.  A  pencil  of  rays  from 

the  object-glass  converg- 
ing towards  a  focus,  a,  is 
brought  to  a  focus,  a', 
half  way  between  the  two 


FIG.  324. 


lenses. 

This  ocular  is  called 


negative  because  it  is  adapted  to  rays  already  converging.  The 
focal  length  of  F  is  three  times  that  of  E,  and  the  distance  between 
the  lenses  is  one-half  the  sum  of  the  focal  lengths. 

The  positive  (or  Ramsden)  ocular  consists  of  two  plano-convex 
lenses,    E   and  E'  (Fig.   325),    with   the   convex  surfaces   turned 
towards  each  other.     These  lenses  are  of  equal  focal  length,  and 
the  distance  between 
them  is  two-thirds  the 
focal  length  of  one  of 
them.      This  combi- 
nation is  not  achro-  o 
matic.        It   is   used 

when  spider  lines  are  placed  in  the  focus  of  the  field  lens  for  pur- 
poses of  exact  measurement; 

In  obtaining  high  magnifying  power,  it  is  generally  best  to  use 
objectives  of  short  focal  length  rather  than  oculars  of  high  power, 
as  the  latter  magnify  the  imperfections  of  the  former. 

386.  Magnifying  power.  —  The  magnifying  power  of  a  com- 
pound microscope  is  the  product  of  the  respective  magnifying 
powers  of  the  object-glass  and  the  eye-piece ;  that  is,  if  the 
first  magnify  20  times  and  the  other  ten  times,  the  total 
magnifying  power  is  200.  The  magnifying  power  is  deter- 


TELESCOPES.  427 

mined  experimentally  by  means  of  a  micrometer  scale,  for  a 
description  of  which  the  student  is  referred  to  technical  works 
on  microscopy. 

387.  Telescopes.  —  Telescopes  are  used  to  view  (scope)  ob- 
jects afar  off  (tele).  They  are  classified  as  astronomical  or 
terrestrial,  according  as  they  are  designed  to  be  used  in  view- 
ing heavenly  bodies  or  terrestrial  objects  ;  reflecting  or  re- 
fracting, according  as  the  objective  is  a  concave  mirror  or  a 
converging  lens.  The  terrestrial  telescope  differs  from  the 
astronomical  in  producing  images  in  their  true  position  with- 
out inversion.  This  is  effected  by  means  of  an  extra  object 
lens,  which  corrects  the  inversion  of  the  main  object  lens. 
The  matter  of  inversion  is  of  little  or  no  consequence  in 
viewing  heavenly  bodies. 

The  refracting  astronomical  telescope  consists  essentially, 


FIG.  326. 

like  the  compound  microscope,  of  two  lenses.  The  object- 
glass  (0,  Fig.  326)  forms  a  real  diminished  image  (a  b)  of  the 
object  A  B  ;  this  image,  seen  through  the  eye-glass  E,  appears 
magnified  and  of  the  size  c  d.  The  object-glass  is  of  large 
diameter,  in  order  to  collect  as  much  light  as  possible  from  a 
distant  object  for  a  better  illumination  of  the  image. 

This  telescope  is  analogous  to  the  microscope,  but  the  two  in- 
struments differ  in  this  respect :  in  the  microscope,  the  object  being 
very  near  the  object-glass,  the  image  is  formed  much  beyond  the 
principal  focus,  and  is  greatly  magnified,  so  that  both  the  object- 
glass  and  the  eye-piece  magnify  ;  while  in  the  telescope,  the  heavenly 
body  being  at  a  great  distance,  the  incident  rays  are  practically 


428  ETHER   DYNAMICS. 

.  parallel,  and  the  image  formed  by  the  object-glass  is  much  smaller 
than  the  object.  The  only  magnification  which  can  occur  is  pro- 
duced by  the  eye-piece,  which  ought  therefore  to  be  of  high  power. 
The  magnifying  power  of  this  instrument l  equals  approximately 
the  focal  length  of  the  object-glass  divided  by  the  focal  length  of  the 
eye-piece. 

388.    The  Newtonian  reflecting  telescope. 

For  an  instrument  of  moderate  cost,  specially  adapted  to  school 
and  college  use  owing  to  the  ease  of  manipulation  and  the  comfort 
with  which  the  observer  may  view  any  part  of  the  sky,  the  New- 
tonian reflecting  telescope  meets  with  much  favor.  It  also  possesses 
the  great  advantage  of  giving  a  colorless  image  of  bright  objects, 


FIG.  327. 


which  cannot  be  obtained  in  a  refractor.2  Fig.  327  represents  a 
horizontal  sectional  view  of  this  instrument.  Incident  rays  are 
reflected  from  the  parabolic  mirror,  M;  striking  the  rectangular 
prism,  m  n,  they  undergo  total  reflection,  and  form  at  a  6  a  small 
image  of  the  heavenly  body.  The  image  is  viewed  through  an  eye>- 
piece  inserted  in  the  side  of  the  telescope.  The  reflector  serves  as 
an  object-glass,  and  is  of  course  free  from  chromatic  aberration, 
while  spherical  aberration  is  corrected  by  the  shape  given  the 


1  The  student  may  ascertain  the  magnifying  power  of  a  terrestrial  telescope  by 
viewing  a  scale  directly  with  one  eye,  and  its  magnified  image  as  seen  through  the 
telescope  with  the  other  eye.     (See  the  author's  Laboratory  Manual  and  Note  Book.) 

2  On  the  whole,  however,  if  the  matter  of  expense  be  disregarded,  the  balance  of 
advantage  is  generally  considered  to  lie  with  the  refracting  telescope.     Briefly,  its 
chief  advantages  are  :  (1)  it  gives  a  brighter  image  than  a  reflector  of  the  same  size  ; 
(2)  it  gives  a  better  definition  ;  (3)  the  lens  does  not  deteriorate  with  age  as  does  the 
speculum  in  a  reflecting  telescope. 

The  largest  refracting  telescope  that  has  thus  far  been  made  (except  the  Yerkes 
telescope  at  the  University  of  Chicago)  is  that  of  the  Lick  Observatory  in  California 
(see  Plate  III). 


PLATE  111. 


PHOTOGRAPHER'S  CAMERA. 


429 


389.  Photographer's  camera.  —  The  photographers  camera 
or  camera  obscura,  of  which  A  B  (Fig.  328)  represents  a  ver- 
tical section,  consists  of  a  dark  box  painted  black  on  the 


FIG.  328. 

interior.  A  screen  of  ground  glass,  S,  forms  a  partition  in 
the  box.  A  sliding  tube,  T,  contains  a  convex  lens,  L.  If 
an  object,  D,  be  placed  some  distance  in  front,  and  the  dis- 
tance of  the  lens  from  the  screen  be  suitably  adjusted,  a 
distinct,  real,  and  inverted  image  can  be  seen  upon  the  screen 
by  looking  through  the  aperture  C.  When  the  image  is  prop- 
erly focused,  the  photographer  replaces  the  ground-glass  plate 
by  a  sensitized  plate,  and  by  their  chemical  power  the  sun's 
rays  imprint  a  true  picture  of  the  object  on  this  plate. 

390.  The  human  eye.  —  Fig.  329  represents  a  horizontal 
section  of  this  wonderful  organ.  Covering  the  front  of  the 
eye,  like  a  watch-crystal,  is  a 
transparent  coat  1,  called  the 
cornea.  A  tough  membrane  2, 
of  which  the  cornea  is  a  con- 
tinuation, forms  the  outer 
wall  of  the  eye,  and  is  called 
the  sclerotic  coat,  or  "  white 
of  the  eye."  This  coat  is 
lined  on  the  interior  with 
a  delicate  membrane  3,  called 
the  choroid  coat ;  the  latter  con- 
sists of  a  black  pigment,  which  FIG.  329. 


430  ETHER    DYNAMICS. 

prevents  internal  reflection.  The  inmost  coat  4,  called  the 
retina,  is  formed  by  expansion  of  the  optic  nerve  0.  The 
muscular  tissue  ii  is  called  the  iris;  its  color  determines 
the  so-called  "  color  of  the  eye."  In  the  center  of  the  iris  is 
a  circular  opening  5,  called  the  pupil,  whose  function  is  to 
regulate,  by  involuntary  enlargement  and  contraction,  the 
quantity  of  light-waves  admitted  to  the  posterior  chamber  of 
the  eye.  Just  back  of  the  iris  is  a  tough,  elastic,  and  trans- 
parent body  6,  called  the  crystalline  lens.  This  lens  divides 
the  eye  into  two  chambers  ;  the  anterior  chamber  7  is  filled 
with  a  limpid  liquid,  called  the  aqueous  humor  ;  the  posterior 
chamber  8  is  filled  with  a  jelly-like  substance,  called  the 
vitreous  humor.  The  lens  and  the  two  humors  constitute  the 
refracting  apparatus. 

Experiment  1.  —  a.  Make  a  model  of  an  eye.  Fill  an  8-ounce  flask 
with  clear  water  (eye-ball).  Cover  one  side  with  black  paper  having  a 
round  hole  in  it  (iris  and  pupil).  Place  a  slightly  convex  lens  in  front  of 
the  hole  (cornea  and  crystalline  lens  combined  ;  the  latter  outside  the 
eye-ball  instead  of  inside).  Place  a  candle  flame  (object)  in  front  of  the 
hole  at  a  distance  of  about  4  feet ;  catch  (inverted)  distinct  image  of  the 
flame  on  a  paper  screen  (retina)  behind  the  flask.  Move  the  candle  nearer 
the  flask  ;  the  image  becomes  indistinct.  Restore  distinctness  by  inter- 
posing a  converging  lens  (remedy  for  long  sight). 

b.  Place  the  candle  very  near  the  lens  and  focus  its  image  on  the 
screen  (now  in  a  new  position).  Move  the  candle  away  ;  the  image  comes 
nearer  the  lens,  and  to  carry  the  image  back  to  the  screen  you  must  use 
a  diverging  lens  (remedy  for  short  sight). 

Experiment  2.  —>  Make  two  dots  on  paper  two  inches  apart.  Close 
the  left  eye,  and  bring  the  right  one  over  the  left  spot.  At  a  distance  of 
about  six  inches  the  right  spot  becomes  invisible.  As  you  bring  the 
paper  nearer,  the  eye  turns  to  regard  the  left  spot ;  the  image  of  the  right 
spot  meantime  travels  noseward  over  the  retina,  until  it  reaches  a  spot 
on  the  retina,  called  the  blind  spot,  which  is  not  sensitive  to  the  action 
of  light-waves.  This  spot  is  where  the  optic  nerve  enters  the  eye. 

The  eye  is  a  camera  obscura,  in  which  the  retina  serves  as 
a  screen.  Images  of  outside  objects  are  projected  by  means 


DEFECTS   OF    VISION.  431 

of  the  crystalline  lens,  assisted  by  the  refraction  of  the 
humors,  upon  this  screen,  and  the  impressions  thereby 
made  on  this  delicate  network  of  nerve  filaments  are  conveyed 
by  the  optic  nerve  to  the  brain.  If  the  two  outer  coatings  be 
removed  from  the  back  part  of  the  eye  of  an  ox  recently 
killed,  so  as  to  render  it  somewhat  transparent,  true  images 
of  whole  landscapes  may  be  seen  formed  upon  the  retina  of 
the  eye,  when  it  is  held  in  front  of  your  eye. 

With  the  ordinary  camera,  the  distance  of  the  lens  from 
the  screen  must  be  regulated  to  adapt  itself  to  the  varying 
distances  of  outside  objects,  in  order  that  the  images  may  be 
properly  focused  on  the  screen.  In  the  eye  this  is  accom- 
plished by  changing  the  convexity  of  the  lens.  We  can  almost 
instantly  and  unconsciously  change  the  lens  of  the  eye,  so  as 
to  form  on  the  retina  a  distinct  image  of  an  object  miles  away 
or  only  a  few  inches  distant.  The  nearest  limit  at  which  an 
object  can  be  placed  so  as  to  form  a  distinct  image  on  the 
retina  is  about  five  inches.  On  the  other  hand,  the  normal 
eye  in  a  passive  state  is  adjusted  for  objects  at  an  infinite 
distance. 

The  retina,  on  careful  examination,  is  found  to  be  com- 
posed in  part  of  little  elements  in  its  back  portion,  which 
have  received,  from  their  appearance,  the  names  of  rods  and 
cones.  It  is  thought  that  these  rods  and  cones  receive  and 
respond  to  the  vibrations  of  ether  ;  in  other  words,  that  they 
co-vibrate  with  the  undulations  of  the  ether,  and  thereby  we 
get  our  sensation  of  light. 

The  eye  is  not  free  from  spherical  or  chromatic  aberration, 
though  these  are  very  much  reduced  by  the  action  of  the  iris, 
which  acts  as  a  diaphragm  to  cut  off  all  except  the  central 
rays. 

391.  Defectsof  vision.— Myopia  (short-sightedness)  is  caused 
by  the  excessive  length  of  the  globe  from  front  to  back,  so 
that  the  images  of  all  but  near  objects  are  formed  in  front  of 


432 


ETHER    DYNAMICS. 


the  retina.  Remedy  :  use  diverging  lenses.  Hypermetropia 
(long-sightedness)  occurs  when  the  axis  of  the  globe  is  so  short 
that  the  image  of  an  object  is  back  of  the  retina  unless  the 
object  is  held  at  an  inconvenient  distance,  in  which  case  it 
tends  to  become  indistinct.  Remedy  :  use  converging  lenses. 
Presbyopia  is  due  to  loss  of  accommodation  power,  so  that  while 
vision  for  distant  objects  remains  clear,  that  for  near  objects 
is  indistinct.  This  defect  is  incident  to  advancing  years,  and 
is  due  to  progressive  loss  of  elasticity  of  the  crystalline  lens. 
Remedy  :  converging  lenses.  Astigmatism  is  caused  by  an 
inequality  in  the  curvature  of  the  cornea  in  different  meridi- 
ans, so  that  when,  for  example,  a  diagram  like  Fig.  330  is 
held  at  a  distance,  vertical  lines  will 
be  in  focus  and  horizontal  lines  will  be 
out  of  focus  and  will  appear  blurred 
and  indistinct,  or  vice  versa.  Remedy: 
lenses  of  cylindrical  curvature.  But, 
for  this,  as  well  as  for  all  other  de- 
fects or  troubles  of  the  eyes,  consult 
a  skilled  oculist,  and  the  earlier  the 
better. 

Advice  to  all :  Do  not  overstrain  or 
overtax  the  eyes,  or  use  them  in  in- 
sufficient or  excessive  light,  in  nickering  light  such  as  that  of 
a  gas-jet,  or  in  unsteady  light  such  as  that  in  a  moving 
vehicle  ;  and  avoid  so  far  as  practicable  sudden  changes  of 
light,  such  as  lightning  flashes,  etc. 

392.  Stereopticon.  —  This  instrument  is  extensively  em- 
ployed in  the  lecture-room  for  producing  on  a  screen  magnified 
images  of  small,  transparent  pictures  on  glass,  called  slides; 
also  for  rendering  a  certain  class  of  experiments  visible  to  a 
large  audience  by  projecting  them  on  a  screen.1  The  lime 


1For  useful  information  relating  to  the  operation  of  projection,  especially  for 
scientific  illustrations,  see  Wright's  Light,  and  Dolbear's  Art  of  Projecting. 


STEREOPT1CON. 


433 


light  is  most  commonly  used,  though  the  electric  light  is  pre- 
ferred for  a  certain  class  of  projections.  The  flame  of  an 
oxyhydrogen  blow-pipe  A  (Fig.  331)  is  directed  against  a 
stick  of  lime  B,  and  raises  it  to  a  white  heat.  The  radiations 


FIG.  331. 


from  the  lime  are  condensed,  by  means  of  a  convex  lens  c, 
called  the  condensing  lens,  (usually  two  plano-convex  lenses 
are  used),  so  that  a  larger  quantity  of  radiations  will  pass 
through  the  convex  lens  E,  called  the  projecting  lens.  The 
latter  lens  produces  (or  projects)  a  real,  inverted,  and  mag- 
nified image  of  the  picture  on  the  screen  S.  The  mounted 
lens  E  may  slide  back  and  forth  on  the  bar  F,  so  as  properly 
to  focus  the  image. 


434 


ETHER    DYNAMICS. 


CHAPTER   II. 

ENERGY  OF  ETHER-STRAIN. —ELECTRO-STATICS. 
SECTION  I. 

INTRODUCTION. 

393.  Electrification.  —  Certain  bodies,  when  the  conditions 
are  suitable,  acquire  by  contact  and  subsequent  separation  (or 
more  readily  by  friction1)  the  property  of  attracting  light 
bodies  such  as  feathers,  pieces  of  tissue  paper,  etc.  For 
example,  glass  rubbed  with  silk,  and  sealing-wax  or  ebonite 
with  woolen  cloth,  manifest  this  property  by  picking  up 
scraps  of  paper,  etc.  Bodies  in  this  state  are  said  to  be 
electrified  or  charged  with  electricity. 

Experiment  1. — Balance  a  flat  wooden  ruler  (Fig.  332)  upon  the  bottom 
of  an  inverted  flask.  Rub  a  rubber  comb  with  a  woolen  cloth  or  draw 

it  a  few  times  through  your  hair  (if  dry) 
and  place  it  near  one  end  of  the  ruler  ; 
the  ruler  will  turn  toward  the  comb. 

Experiment  2.  —  Hold  the  comb  over  a 
handful  of  bits  of  tissue  paper  ;  the  papers 
quickly  jump  to  the  comb,  stick  to  it  for 
an  instant,  and  then  leap  energetically 
from  the  comb.  The  papers  are  first 
attracted  to  the  comb,  but  in  a  short 
time  acquire  some  of  its  electrification, 
and  then  are  repelled.  If  the  papers  be 
pulled  off  from  the  comb,  they  will  cling 
FIG.  332.  to  the  hands  of  the  operator. 


1  Possibly  because  in  the  act  of  rubbing  more  points  are  brought  in  contact. 


TWO    KINDS    OF    ELECTRIFICATION. 


435 


FIG.  333. 


394.    Two  lands  of  electrification. 

Experiment  3.  —  Suspend  a  ball  of  elder  pith,  C  (Fig.  333),  by  a  silk 
thread.  Electrify  a  glass  rod  D  with  a  silk  handkerchief  and  present  it  to 
the  ball  ;    attraction   at   first 
occurs,  followed  by  repulsion 
soon  after  contact.     Next  ex- 
cite a  stick  of  sealing-wax  or 
a  rubber  comb  with  a  woolen 
cloth  and  present  it  to  the  ball 
which  is  repelled  by  the  elec- 
trified glass  ;  it  is  attracted  by 
the  electrified  wax  or  rubber. 
Experiment    4.  —  Suspend 
in  two  stirrups  two  glass  rods 
that  have  each   been  rubbed 
with  silk  (Fig.  334),  and  pre- 
sent them  to  each  other;  they 
repel  each  other.    Suspend  two  sticks  of  sealing-wax  that  have  been  rubbed 
with  flannel  in  the  same  manner;  the  same  result  follows.     Now,  in  a 

like  manner,  present  one  of  the  glass  rods 
and  one  of  the  sticks  of  sealing-wax  to 
each  other  ;  they  attract  each  other. 

It  is  evident  (1)  that  there  are 
two  kinds  or  conditions  'of  electrifi- 
cation;  or,  for  convenience,  we 
sometimes  say  two  kinds  of  elec- 
tricity;  (2)  that  bodies  similarly 
electrified  repel  one  another,  bodies  oppositely  electrified  attract 
one  another. 

Glass  rubbed  with  silk  is  said  to  receive  a  charge  of  vitreous 
electrification  ;  the  wax,  after  being  rubbed  with  woolen  cloth, 
on  the  other  hand,  is  charged  with  resinous  electrification. 
Vitreous  and  resinous  electrifications  bear  to  each  other 
somewhat  the  same  relation  as  positive  and  negative  quanti- 
ties in  algebra  ;  and  by  arbitrary  convention  vitreous  charges 
are  said  to  be  positive  (written  -f~E),  and  resinous  negative 
(written  — E). 


FIG.  334. 


436  ETHER    DYNAMICS. 

Experiment  5.  — Once  more  electrify  a  stick  of  sealing-wax  with  woolen 
cloth,  and  present  it  to  the  pith  ball,  and  after  the  ball  is  repelled,  bring 
the  surface  of  the  flannel  which  had  electrified  the  rod  near  the  ball ;  the 
ball  is  attracted  by  it,  showing  that  the  rubber  is  also  electrified,  and 
with  the  opposite  kind  to  that  which  the  sealing-wax  possesses. 

One  kind  of  electrification  is  never  developed  alone  ;  when 
two  substances  are  rubbed  together,  and  one  becomes  electri- 
fied, electrification  of  the  opposite  kind  is  always  developed 
in  the  other. 

395.  Electric   attraction   and  repulsion   explainable  on    the 
hypothesis  of  ether-strain.  —  When  small   pieces  of  glass  and 
silk  are  rubbed  together,  it  is  found  that  after  they  are  pulled 
apart  they  attract  each  other  with  a  definite  and  measurable 
force ;  and  that  this  force  varies   inversely  as   the   square    of 
the  distance  between  them.    When  two  bodies  are  pulled  apart, 
energy  is  expended  upon  them  which  will  be  restored  when 
they  are  allowed  to  approach  each  other.     This  phenomenon 
is  explainable  on  the  hypothesis  that  in  the  work  of  separa- 
tion, the  ether  between  or  around  them  is  strained  j  and  that 
the  tendency  of  the  two  bodies  to  approach  each  other  is  the 
tendency  of  the  elastic  ether  to  recover  its  normal  condition. 
The  phenomena  of  electric  attraction  and  repulsion  are  most 
satisfactorily  explained  on  the  hypothesis  of  ether-strain.    By 
whatever  hypothesis  explained,  it  is  certain  thsit^lectri^c^mL 
i,<?  the  result  nf  iimyf?  done,  and  is  a  form  of  potential  energy 

396.  What  is  electricity  ?  —  The  student  naturally  has  al- 
ready  begun  to  ask  the  never-answered  question,  "What  is 
electricity  ?"  and  to  inquire,  "  What  is  the  function  of  electri- 
city in  these  operations  ?  "   Provisionally  we  shall  regard  elec- 
tricity as  that  which  is  transferred  from  one  body  to  another 
body  when  the  two  become  oppositely  electrified.1    Electricity 

1  What  the  ultimate  nature  of  electricity  is,  whether  it  be  the  ether  itself  or 
(more  probably)  a  constituent  of  the  ether  "  as  water  is  a  constituent  of  jelly "  ; 
whether  it  be  a  fluid  (it  certainly  possesses  the  property  of  fluidity) ;  whether,  accord- 
ing to  Franklin,  a  positive  charge  is  an  excess  and  a  negative  charge  a  deficit  in  a 


QUANTITY    OF    ELECTRICITY.  437 

is  not  a  form  of  energy.1  It  is  quite  true  that  electricity 
under  pressure  or  in  motion  possesses  energy  ;  in  the  same 
sense  do  water  and  air  under  like  conditions  possess  energy, 
but  we  do  not  therefore  deny  them  to  be  forms  of  matter. 
Electricity,  rather,  in  many  respects  possesses  the  nature  of 
matter.  Like  matter  it  can  neither  be  created  nor  annihil- 
ated, and  like  matter  it  can  be  moved  and  put  under  stress. 
For  present  purposes,  then,  electrification  may  be  regarded  as 
a  state  of  strain  in  some  intervening  medium  produced  by  a 
transfer  of  electricity  from  one  body  to  another  and  the  sub- 
sequent separation  of  the  two  bodies.  Electrification  is  the 
result  of  work  done,  and  is  most  certainly  a  form  of  energy. 

397.  Quantity  of  electricity. 

When  we  do  not  know  what  a  thing  is,  it  is  difficult  to  conceive 
a  definite  quantity  of  it.  But  our  knowledge  of  electricity  like  that 
of  force  is  derived  from  its  effects.  From  the  measurement  of  its 
effects,  therefore,  can  we  define  a  unit  quantity  of  electricity.  For 
purposes  of  calculation  at  least,  electricity  of  either  kind  may  be 
treated  precisely  as  if  it  were  a  material  incompressible  fluid,  and 
any  increase  or  decrease  of  electrification  may  be  considered  to  be 
produced  by  the  addition  or  taking  away  of  a  quantity  of  electricity. 
Quantities  of  electricity  are  added  and  subtracted  by  the  usual  rules 
of  algebra,  the  kinds  of  electrification  being  denoted  by  the  +  and 
—  signs. 

398.  Law  of  attraction. 

When  two  equally  electrified  bodies  attract  or  repel  each  other/ 
with  a  force  of  one  dyne  at  a  distance  of  one  centimeter  in  air,  eacW 
is  charged  with  a  certain  definite  quantity  which  may  be  taken  aa 
a  unit  quantity  of  electricity.  If  two  bodies  repel  or  attract  each 

certain  standard  quantity  of  the  fluid  which  all  bodies  are  supposed  to  possess  in 
their  unexcited  state  ;  or  whether  (more  probably)  positive  and  negative  electricities 
are  distinct  entities  (whose  relations  to  each  other  are  more  like  those  of  sodium 
and  chlorine  than  like  those  of  heat  and  cold),  such  that  when  combined  in  any 
body  they  neutralize  each  other  so  that  the  body  possesses  none  of  the  properties  of 
electrification,  but  when  they  by  any  means  become  separated  two  separate  portions 
of  matter  always  become  oppositely  charged  —  are  questions  too  recondite  for  dis- 
cussion in  any  general  work  on  physics.  Consult  "  Modern  Views  of  Electricity," 
by  O.  J.  Lodge. 

1  See  Darnell's  Principles  of  Physics,  p.  530. 


488 


ETHER   DYNAMICS. 


other  with  some  other  intensity,  the  quantities  with  which  they  are 
charged  are  easily  determined.  For  example,  suppose  that  a  body 
charged  with  three  units  is  attracted  at  a  distance  of  one  centimeter 
by  one  charged  with  six  units.  The  total  attraction  of  the  six  units 
of  the  second  body  for  each  one  of  the  other  three  is  obviously 
expressed  by  six,  giving  a  total  attraction  of  6x3=18  dynes. 
It  is  evident  that  if  any  two  of  these  three  quantities  be  known, 
the  third  can  be  determined. 

Again,  suppose  that  the  attraction  (or  repulsion)  be  at  some  other 
distance,  the  force,  being  a  radiant  one,  varies  inversely  as  the  square 
of  the  distance  ;  consequently,  to  determine  this  force  the  product  of 
the  two  quantities  must  be  divided  by  the  square  of  the  distance 
between  them.  Now  if  we  substitute  quantities  of  electricity,  q  and 
#',  for  masses  m  and  m'  in  the  formula  for  attraction  of  gravitation 
(§  96),  we  shall  have  the  formula  for  electrical  attraction  (or  re- 


pulsion) A  ;  viz.  A  = 


in  which  k  is  the  dielectric  constant 


(see  §  409).  That  is,  the  electrical  attraction  between  two  charged 
bodies  (provided  the  areas  of  the  bodies  are  small  so  as  to  keep 
them  under  the  law  of  radiant  force)  varies  as  the  products  of  their 
charges  and  inversely  as  the  square  of  the  distance  between  them. 

399.  Electroscope.  —  This  is  an  instrument  used  to  detect 
the  presence  of  electrification  in  a  body,  and  to  determine  its 
kind.  It  usually  consists  of  two  strips  of  gold  foil,  A  B  (Fig. 

335),  suspended  from  a  brass 
rod  within  a  glass  jar.  To 
the  upper  end  of  the  rod  is 
fixed  a  metal  disk,  C.  On 
the  opposite  sides  of  the  in- 
terior of  the  jar  are  two  strips 
of  metal  foil,  D  and  E,  of  suf- 
ficient hight  to  be  touched  by 
the  strips  A  and  B  on  their 
extreme  divergence. 

(1)  If  an  unelectrified  body 
be  brought  near  the  disk  C, 
FIG  335  no  change  takes  place  in  the 


CONDUCTION.  439 

two  strips  of  foil  A  and  B,  but  if  an  electrified  body  be 
brought  near  the  disk,  the  strips  diverge,  thus  indicating  the 
existence  of  a  charge  of  electricity  in  the  body. 

(2)  If  the  electroscope  be  charged  by  contact  with  an  ex- 
cited body,  the  strips  will  remain  in  a  divergent  position. 
While  in  this  condition,  if  a  body  similarly  charged  be 
brought  near  the  disk,  the  strips  will  diverge  more;  but  if 
an  unexcited  body,  or  a  body  oppositely  electrified  be  brought 
near  the  disk,  the  strips  will  collapse. 

400.    Conduction. 

Experiment  6.  —  a.  Rub  a  brass  tube,  held  in  the  hand,  with  warm 
silk.  Bring  it  near  the  disk  of  the  electroscope  ;  the  leaves  are  unaffected. 
6.  Wrap  a  piece  of  sheet  rubber  around  one  end  of  the  tube  and  hold  this 
end  in  the  hand,  and  rub  as  before.  Bring  it  near  the  disk  of  the  elec- 
troscope ;  notice  that  the  leaves  diverge,  c.  Repeat  the  last  operation  ; 
but  before  bringing  the  tube  near  the  disk  touch  the  tube  with  a  finger. 
The  leaves  no  longer  show  signs  of  electrification. 

In  the  first  (a)  and  last  (c)  operations  electricity  escaped 
through  the  hand  and  body  to  the  earth  ;  in  the  second  (b)  it 
was  prevented  from  escaping  by  the  intervening  sheet  rubber. 
Substances  which  allow  electricity  to  spread  over  them,  i.e. 
substances  which  offer  little  resistance  to  the  flow  of  elec- 
tricity, are  called  conductors.  Those  which  offer  great  resist- 
ance to  its  passage  are  called  non-conductors,  insulators,  or 
dielectrics. 

Some  of  the  best  insulating  substances  are  dry  air,  ebonite, 
shellac,  resins,  glass  (free  from  lead,  e.g.  common  bottle  glass), 
silks,  and  furs.  On  the  other  hand,  metals  are,  as  a  class, 
exceedingly  good  conductors.  Moisture  injures  the  insulation 
of  bodies  ;  hence  experiments  succeed  best  on  dry,  cold  days 
of  winter,  when  moisture  of  the  air  is  least  liable  to  be  con- 
densed on  the  surfaces  of  apparatus,  especially  if  it  be  kept 
warm. 

Water  cannot  be  retained  in  a  reservoir  unless  its  walls  be 
of  sufficient  strength  ;  so  a  body,  in  order  to  become  charged 


440 


ETHEK    DYNAMICS. 


and  to  retain  the  charge,  must  be  surrounded  by  something 
that  will  offer  sufficient  resistance  to  the  escape  of  electricity. 
As  regards  a  specific  body,  there  is  no  limit  to  the  quantity  of 
electricity  with  which  it  can  be  charged,  provided  the  charge 
can  be  retained.  This  entity  which  represents  the  walls  of  the 
reservoir  is  termed  the  dielectric.  It  may  be  the  air  1  or  any 
of  the  so-called  non-conductors  of  electricity.  Even  the  ether 
may  be  considered  a  dielectric.  A  body  thus  surrounded  is 
said  to  be  insulated. 

Experiment  7.  —  Prepare  an  insulated  stool  by  placing  a  board  on  four 
dry  and  clean  glass  tumblers,  used  as  legs.  Let  a  person,  whom  we  will 
call  John,  stand  on  this  stool,  and  hold  in  one  hand  one  end  of  a  wire 
(say)  4  yds.  long,  the  other  end  of  which  is  attached  to  the  disk  of  an 

electroscope.  a.  Let  a 
second  person,  James, 
strike  John  with  a  cat's 
fur ;  the  leaves  diverge. 
6.  Substitute  a  white  silk 
thread  for  the  wire,  touch 
the  electroscope  with  a 
finger  so  as  to  discharge 
it,  and  repeat  the  last  op- 
eration ;  the  leaves  do  not 
diverge.  c.  Let  James 
strike  John  several  times 
with  the  fur,  and  then 
bring  a  finger  knuckle 
near  to  some  part  of 
John's  person,  e.g.  the 
chin,  nose,  or  a  knuckle 
(Fig.  336);  an  electric  spark  will  pass  between  the  two  and  both  will 
experience  a  slight  shock.  The  electricity  which  had  accumulated  on 
John  in  consequence  of  his  insulation,  escapes  or  is  discharged  through 
James. 

1  If  the  air  were  a  conductor  of  electricity,  a  body  could  not  be  charged  in  it; 
there  could  be  no  thunder  storms,  and  man  would  probably  never  have  known  of  the 
existence  of  electricity. 


FIG.  336. 


ELECTRICITY    ACTS    ACROSS    A    DIELECTRIC.          441 


SECTION  II. 
INDUCTION. 

401.  Electricity  acts  across  a  dielectric. 

Experiment  1.  —  Fig.  337  represents  an  empty  egg-shell  covered  with 
tin  foil  to  make  it  a  good  conductor.  It  is  suspended  from  a  glass  rod 
by  a  silk  thread,  a.  Electrify  a 
glass  rod  and  bring  it  near  the 
shell.  The  shell  moves  toward  the 
rod.  6.  Next  introduce  a  glass 
plate  between  the  rod  and  shell. 
The  shell  approaches  the  rod  as 
before. 

The  chief  lesson  we  learn 
from  this  experiment  is  that 
electricity  acts  across  a  dielec- 
tric.1 In  a  the  dielectric  was 
air  ;  in  b,  air  and  glass. 

402.  To  determine  what  ac- 
tually happens  on  an  insulated 
conductor  when  an  electrified 
body  is  brought  near. 

Experiment  2.  —a.  Suspend,  as  above,  two  shells  so  as  to  touch  each 
other,  end  to  end,  as  in  Fig.  338,  thus  making  practically  one  conductor. 
Bring  near  to  one  end  of  the  shells  a  sealing-wax  rod,  D,  excited  with 
—  E.  While  the  rod  is  in  this  position  carry  a  thin  strip  of  tissue  paper, 
C,  along  the  shells.  The  paper  is  attracted  to  the  shells,  but  most 
strongly  at  the  ends.  In  the  middle  of  the  conductor,  where  the  shells 
touch  each  other,  there  is  little  if  any  electrification. 

6.  While  the  rod  D  is  still  in  position,  separate  B  from  A,  then  remove 
I).  Test  each  shell  with  the  tissue  paper  ;  both  are  found  to  be  excited. 

c.  Charge  an  electroscope  with  +E.  Then  bring  A  near  it ;  the  leaves 
diverge,  showing  that  A  is  charged  with  +  E.  Bring  B  near  the  electro- 
scope ;  the  leaves  collapse,  showing  that  B  is  charged  with  —  E. 


Fro.  a37. 


1  Insulators  across  which  electric  action  takes  place  are  called  dielectrics,  from 
the  Greek  did,  across. 


442 


ETHER   DYNAMICS. 


d.  Finally  bring  the  two  shells  near  each  other ;  they  attract  each 
other.  Allow  them  to  touch  each  other,  and  then  test  each  with  the 
tissue  paper  or  the  electroscope ;  it  will  be  found  that  both  have  become 
discharged. 

From  the  above  operations  we  learn  that  when  an  electri- 
fied body  is  brought  near  but  not  in  contact  with  an  insulated 


FIG.  338. 


conductor,  the  electrified  body  acts  across  the  dielectric  upon 
the  conductor,  repelling  electricity  of  the  same  kind  to  the 
remote  side  of  the  conductor,  and  attracting  the  opposite  kind 
to  the  side  near  to  it.  Such  electrical  action  is  called  induc- 
tion. The  electrified  body  which  produces  the  action  is  called 
the  inducing  body  ;  the  charge  of  electricity  thus  produced  is 
called  induced  electricity. 

403.    Charging  by  induction. 

Experiment  S.  —  Take  a  proof  plane  E  (Fig.  339)  (which  consists  of  an 
insulating  handle  of  glass  or  gutta  percha,  terminating  at  one  end  with  a 
thin  metal  disk,  F,  about  the  size  of  a  5-cent  nickel),  and  connect  it  with 
an  electroscope,  G,  by  a  fine  wire,  H.  Bring  a  stick  of  sealing-wax 
electrified  as  before  with  —  E  near  the  egg-shell  conductor.  Holding 
the  proof  plane  by  the  insulating  handle,  bring  the  disk  near  the  end  of 
the  conductor  charged  by  induction  with  —  E.  The  — E  will  act  induc- 
tively upon  the  continuous  conductor  consisting  of  disk,  wire,  and 
electroscope,  charging  the  end  nearest  itself  (i.e.  the  disk)  with  +E  and 


CHARGING    BY    INDUCTION. 


443 


f^"       T 

F  -A- 


FIG.  339. 


the  remote  end  (i.e.  the  leaves)  with  *-E.  The  leaves  of  the  electro- 
scope show  the  presence  of  a  charge  by  their  divergence. 

Now  while  everything  is  in  the  position  indicated  by  the  cut,  touch 
with  the  finger  any 
part  of  the  continu- 
ous conductor ;  the 
leaves  of  the  electro- 
scope instantly  col- 
lapse. The— E  with 
which  the  leaves  had 
been  charged  being 
free  is  discharged 
through  your  body. 
But  the  +  E  concen- 
trated on  the  disk  of 
the  proof  plane  is 

bound  by  the  attraction  of  the  charge  of  —  E  on  the  end  of  the  shell 
nearest  it,  and  cannot  escape.  Remove  the  finger  from  the  electroscope 
and  the  proof  plane  from  the  influence  of  the  shell;  the  leaves  again  diverge. 

The  last  phenomenon  is  explained  as  follows  :  After  —  E 
had  .been  discharged  from  the  continuous  conductor,  there 
was  left  an  excess  of  +E;  but  this  excess  was  all  concen- 
trated in  the  disk  F  so  long  as  it  remained  near  the  negative 
charge  of  the  shell.  But  as  soon  as  F  was  removed  from  the 
influence  of  the  shell,  the  charge  spread  itself  over  the  entire 
conductor,  and  the  leaves,  which  received  a  portion  of  the 
charge,  diverged.  The  conductor  is  said  to  be  charged  by 
induction. 

Experiment  4.  —  To  electrify  the  shell  by  induction,  bring  the  excited 
wax  near  it,  touch  the  shell  with  a  finger,  remove  the  finger,  and  finally 
remove  the  rod.  The  proof  plane  being  connected  with  the  electroscope 
and  being  charged  with  —  E,  bring  F  near  to  the  shell  A ;  the  leaves 
collapse,  showing  that  the  shell  is  charged  with  +E,  which  draws  the 
— E  away  from  the  leaves. 

Observe  that  when  a  body  becomes  charged  by  induction 
the  charge  which  it  receives  is  opposite  in  kind  to  that  of  the 
inducing  body. 


444  ETHEK    DYNAMICS. 

404.  Charging  by  conduction. 

Experiment  5.  —  Disconnect  the  proof-plane  from  the  electroscope. 
Charge  the  electroscope  with  —  E  and  the  shell  with  +E  ;  touch  the 
shell  with  the  disk  of  the  proof  plane,  then  hold  the  disk  near  the 
electroscope  ;  the  divergent  leaves  collapse,  showing  that  the  disk  bears 
+  E  which  it  received  by  conduction  from  the  shell  when  they  were 
brought  in  contact.  Of  course  the  charge  is  the  same  kind  as  that  of  the 
body  which  communicated  it. 

405.  Induction  precedes  attraction.  - —  When  a  pith  ball  is 
brought  near  an  electrified  glass  rod,  the  -f  E  on  the  rod  A 

(Fig.  340)  induces  —  E  on  the  side  of  the  ball  B 
nearest  A  and  repels  -J-E  to  the  farther  side. 
The  +  E  of  A  and  the  —  E  of  B  therefore  attract 
each  other  ;  likewise  the  -f-E  of  A  and  the  -fE 
of  B  repel  each  other  ;  but  since  the  former 
charges  are  nearer  each  other  than  the  latter 
are,  the  attraction  exceeds  the  repulsion. 
F  406.  Electrification  confined  to  the  outside  sur- 

face of  a  conductor.     Metal  screens. 

Experiment  6. — Place  a  tin  cup,  A  (Fig.  341),  on  a  glass  tumbler 
coated  with  shellac  and  charge  it  heavily  with  electricity  from  an  electri- 
cal machine  (see  Section  V.).  Introduce  a  proof- 
plane  into  the  cup  and  touch  the  interior  surface  of 
the  cup.  Remove  the  proof-plane  and  place  it  near 
the  electroscope ;  the  leaves  of  the  electroscope  are 


If  a  solid  metal  ball,  A  (Fig.   342),  sus- 
pended by  an  insulating  thread,  be  electrified 
and   then   covered  with   two   hemispherical 
metallic  cups,  B  and  Cf  having   insulating 
handles,    and   the    cups    be    afterwards    re- 
moved, the  ball  when  tested  with  the  elec- 
troscope will  be  found  to  have  lost  all  its  charge,  while  the 
cups  will  be  found  to  be  charged.     It  does  riot  make  the 
slightest   difference  as  to  the  result   Avhether  an  insulated 


FIG.  342. 


"FARADAY'S  ICE-PAIL  EXPERIMENT."          445 

conductor  be  solid  or  hollow.     Wood  covered  with  tin-foil 
answers  the  purpose  as  well  as  any  other  body. 

If  a  hollow  conductor  be 
charged,  however  highly, 
with  electricity,  the  whole 
of  the  charge  is  found 
upon  the  outside  surface. 
If  the  electroscope  in 
the  last  experiment  were 
placed  inside  the  tin  cup, 
or  if  it  be  set  inside  a  vessel  of  wire  gauze  (e.g.  a  bird  cage), 
and  the  vessel  be  charged  with  electricity  or  a  heavily 
charged  body  be  brought  near  the  vessel,  the  electroscope  will 
be  unaffected.  This  interesting  and  important  fact  shows 
that  a  metallic  shell,  however  thin,  entirely  screens  bodies  inside 
it  from  external  electrification,  however  great.1 

407.    "  Faraday's  Ice-pail  Experiment." 

Experiment  7.  —  a.  Insulate  well  a  tin  pail  (Fig.  343)  and  connect  it 
with  an  electroscope.  Charge  heavily  a  metal  ball  suspended  by  an  in- 
sulating thread,  with  (say)  -fE.  Lower 
the  ball  within  the  pail ;  the  pail  be- 
comes charged  by  induction,  inside 
with  —  E  and  the  outside  (together  with 
the  electroscope)  with  +E.  The  leaves 
of  the  electroscope  diverge. 

b.  Touch  the  outside  of  the  pail  with 
a  finger ;  the  free  charge  of  +  E  escapes 
to  the  earth  (see  §  413),  and  the  leaves 
of  the  electroscope  collapse.  Remove 
the  finger  and  then  withdraw  the  ball 
slowly  frohi  the  pail ;  the  leaves  of  the 
electroscope  slowly  diverge,  and  remain  diverged  after  the  ball  is  removed. 

1  To  test  this  still  further,  Faraday  built  a  cubical  cage  of  12  ft.  edge,  of  copper 
wire,  and  lined  the  interior  with  paper  covered  with  tin-foil.  This  chamber  was  in- 
sulated and  put  in  connection  with  a  powerful  electrical  machine  while  working. 
He  says  :  —  "  I  went  into  the  cube  and  lived  in  it,  using  electrometers  and  all  other 
tests  of  electrical  states  ;  I  could  not  find  the  least  influence  upon  them,  though  all 
the  time  the  outside  of  the  cube  AVHS  powerfully  charged,  and  large  sparks  and 
brushes  were  darting  from  every  part  of  its  outer  surface." 


FlG.  343. 


446  ETHER    DYNAMICS. 

c.  The  ball  is  now  charged  with  +  E  and  the  pail  with  —  E.  Bring 
the  ball  in  contact  with  the  pail ;  the  leaves  of  the  electroscope  completely 
collapse,  showing  that  the  +E  and  the  — E  have  combined,  neutralizing 
each  other  and  leaving  no  excess  of  either.  Hence  we  conclude  that  the 
positively  charged  ball  when  lowered  into  the  pail  must  have  induced  an 
equal  charge  of  —  E  in  the  pail.  This  is  generally  called  the  Ice-pail 
Experiment  because  Faraday  in  the  original  experiment  used  an  ice-pail. 

The  amount  of  opposite  electricity  induced  on  surrounding 
conductors  by  an  electrified  body  is  equal  to  the  body's  own  charge. 
One  body  cannot  be  charged  with  a  quantity  of  -{-E  without 
an  equal  charge  of  — E  being  established  somewhere  else,  and 
vice  versa.  The  student  will  bear  in  mind  that  whenever  in 
his  experiments  he  charges  any  body  with  electricity,  an 
equal  complementary  charge  always  exists  distributed  over 
neighboring  objects  or  on  the  walls  of  the  room.  When  a 
thunder-cloud  is  charged  it  has  its  equal  complementary 
charge  in  the  part  of  the  earth  nearest  it.  The  sum  total 
of  all  the  +E  and  — E  in  existence  is  zero. 

408.  Definition  of  electro-static  induction.  —  We  are  now  in 
a  position  to  understand  the  following  definition  :  Electro- 
static induction  is  the  action  whereby  a  charged  body  surrounded 
by  a  dielectric  evokes  an  equal  and  opposite  charge  on  the  inner 
surface  of  the  enclosure  containing  the  body  and  the  dielectric. 

409.  Inductive  capacity.  —  The  power  of  transmitting  in- 
duction varies  with  different  substances.     Across  glass,  sul- 
phur, and  shellac  the  effect  produced  by  an  electrified  body  is 
different  from  that  across  air,  the  distance  being  the  same. 
The  power  of  a  dielectric  substance  to  receive  and  transmit 
that  electric  strain  which  we  call  induction  depends  on  the 
specific  inductive  capacity  of  the  substance. 

When  we  electrify  a  body,  a  certain  quantity  of  energy  is 
expended,  and  this  is  regarded  as  the  energy  of  the  electric 
charge,  and  may  be  recovered  by  discharging  the  body.  The 
energy  is,  however,  stored  in  the  ether  around  the  body  said 
to  be  charged. 


ELECTRIC    DENSITY. 


447 


SECTION  III. 


DISTRIBUTION    OF    ELECTRICITY. 

410.  Electric  density.  —  The  following  experiments  by  no 
means  give  exact  quantitative  measurements,  but  they  are 
suitable  for  our  purpose. 

Experiment  1.  —  a.  Charge  a  well-insulated  metal  sphere  with  +  E. 
Touch  some  point  on  the  surface  with  a  proof-plane  and  bring  it 
in  contact  with  an  uncharged  electroscope.  Notice  the  amount  of 
divergence. 

6.  Discharge  the  proof-plane  and  electroscope  and  touch  a  different 
point  on  the  sphere  with  the  proof-plane,  and  touch  the  electroscope  as 
before.  Notice  that  there  is  equal  divergence  of  the  leaves. 

Experiment  2.  —  a.  Electrify  an  insulated  pear-shaped  conductor  (Fig. 

344).  Touch  the  larger  end 
of  the  conductor  with  a  proof- 
plane  and  bring  it  in  contact 
with  an  electroscope.  Notice 
the  amount  of  divergence  of 
the  leaves. 

6.  Discharge  the  proof-plane 
and  electroscope.  Touch  the 
pointed  end  ;  notice  that  on 
bringing  the  proof-plane  in 
contact  with  the  electroscope 
the  divergence  of  the  leaves  is 
greater  than  before.  In  this 
case,  therefore,  the  charge  is  not  uniformly  distributed. 


FIG.  344. 


We  conclude  that  the  electricity  is  of  equal  density  on  the. 
sphere,  but  of  unequal  density  on  the  pear-shaped  conductor. 
Electric  density  is  defined  as  the  quantity  of  electricity  on  a 
body  per  unit  area. 

It  follows,  from  this  definition,  that  if  the  surface  be 
increased,  the  quantity  of  electricity  being  the  same,  the 
density  is  diminished,  and  vice  versa.  The  relation  between 


448 


ETHER    DYNAMICS. 


density  and  area  is  readily  shown  in  the  following  manner  : 
Suspend  a  sheet  of  tin  foil 
from  a  glass  rod  (Fig.  345), 
connect  the  lower  end  of  the 
foil  with  an  electroscope,  and 
charge  the  foil  lightly.  Roll 
the  foil  up  on  the  rod,  and  as 
the  surface  becomes  reduced 
the  leaves  diverge  more  widely. 
Distribution  of  electrifica- 
tion, or  the  electric  density  at 
different  points  on  a  conductor,  depends  on  its  shape.  In 
Fig.  346  the  distances  between  the  surfaces  of  the  bodies  and 
the  dotted  lines  are  intended  to  represent  approximately  the 
relative  densities  at  different  parts  of  each  body. 


FIG.  345. 


FIG.  346. 

411.  Effect  of  points. — As  bodies  become  pointed,  the  elec- 
tric density  increases  at  the  pointed  end,  until  it  becomes 
so  great  that  the  electricity  is  discharged.  The  particles  of 
air  surrounding  the  point  become  heavily  charged  and  are 
repelled ;  other  particles  rush  in  to  take  their  place,  and  they 
in  turn  are  electrified  and  repelled.  A  current  of  air  pro- 
ceeding from  the  point,  called  the  "  electric  wind,"  is  thus 
produced,  and  the  conductor  becomes  discharged  by  a  process 


ELECTROSTATICS    AND    ELECTROKINETICS.  449 

somewhat  analogous  to  convection  of  heat.  Points  or  sharp 
edges  on  a  conductor  cause  a  continuous  loss  of  electricity, 
and,  therefore,  must  be  carefully  avoided  in  all  apparatus 
where  they  are  not  essential. 


SECTION  IV. 

ELECTRICAL    POTENTIAL. 

412.  Electrostatics  and  electrokinetics.  —  Electricity  may  be 
at  rest,  as  in  a  charged  body,  or  it  may  be  in  motion,  as  in 
the  case  of  a  charged  body  "connected  by  a  conductor  with  the 
earth,  when  it  is  discharged  through  the  conductor  to  the  earth. 
It  will  be  shown  later  on  that  as  long  as  a  flow  of  electricity 
continues  the  conductor  along  which  it  flows  has  properties 
different   from   those   of   a   simple   electrified   body.      That 
branch  of  electrical  science  which  treats  of  the  properties 
of   simple    electrified    bodies  is  called  Electrostatics,  because 
in  them  electricity  is  supposed  to  be  at  rest ;  and  that  branch 
which  treats  of  electricity  in  motion  is  called  Electrokinetics. 

413.  Potential. --The  fundamental  fact  of   electricity  is 
that  we  are  able  to  place  bodies  in  different  electrical  con- 
ditions.    A  charge  of  electricity,  which  implies  an  abnormal 
electrical  condition,  is  the  foundation  of  all  electrical  phe- 
nomena.    We  are  now  to  discuss  in  a  very  simple  manner 
the  meaning  and  use  of  the  very  important  term  potential 
with  reference  to  electricity. 

a.  When  a  charged  conductor  is  connected  with  the  earth, 
a  transfer  of  electricity  takes  place  between  the  body  and 
the  earth. 

b.  If  the  body  be  charged  w  ith  -+-  E,  we  say  arbitrarily  that 
electricity  passes  to  the  earth ;  but  if  the  body  be  charged 
with  —  E,  electricity  passes  from  the  earth  to  the  body. 

c.  If  two  insulated  charged  conductors  be  connected  with 


450  ETHER    DYNAMICS. 

each  other,  electricity  may  or  may  not  pass  from  one  to  the 
other.  Now  whether  electricity  passes  from  one  to  the  other, 
and  in  what  direction  it  passes,  if  at  all,  depends  upon  the 
so-called  potentials  of  the  conductors. 

d.  If  two  bodies  have  the  same  potential  no  transfer  of 
electricity  takes  place  between  them  when  they  are  connected 
by  a  conductor ;  but  if  the  two  bodies  have  different  poten- 
tials, there  will  be  a  transfer,  and  the  body  from  which  the 
electricity  flows  is  said  to  be  at  a  higher  potential  than  the 
one  to  which  it  flows. 

414.  Definition  of  potential.  —  The  potential  of  a  conductor 
may,  therefore,  be  defined  provisionally  as  the  electrical  con- 
dition of  that  conductor  which  determines  the  direction  of 
the  transfer  of  electricity. 

The  term  potential  is  relative,  i.e.  we  compare  the  potential 
of  one  body  with  that  of  another. 

It  is  important  to  have  a  standard  of  reference  whose  po- 
tential is  considered  to  be  zero,  just  as  it  is  convenient  in 
stating  the  elevations  and  depressions  of  the  earth's  surface 
to  give  the  distances  above  or  below  sea-level,  which  is  taken 
as  the  zero  of  hight.  For  experimental  purposes  the  earth  is 
usually  assumed  to  be  at  zero  potential.  A  body  charged 
with  -j-E  is  understood  to  be  one  that  has  a  higher  potential 
than  that  of  the  earth,  and  a  body  charged  with  — E  is  one 
that  has  a  lower  potential  than  that  of  the  earth. 

415.  Analogies.  —  Potential  is  analogous,  in  many  respects, 
to  (1)  temperature,  and  (2)  liquid  level. 

(1)  When  we  say  that  the  temperature  of  air  is  20°  or 
—  10°  C,  we  mean  that  its  temperature  is  20°  above  or  10° 
below  the  standard  temperature  of  reference,  viz.  that  of 
melting  ice.  If  two  bodies  at  different  temperatures  be 
placed  in  thermal  communication,  heat  will  pass  from  the 
body  at  a  higher  temperature  to  the  one  at  a  lower,  and  will 
continue  to  do  so  until  both  are  at  the  same  temperature. 


ELECTRICAL   CAPACITY.  451 

(2)  If  two  vessels,  containing  water  at  different  levels,  be 
put  in  communication  at  their  bottoms  by  a  pipe,  water  will 
flow  from  the  one  at  a  higher  level  to  the  one  at  a  lower  until 
the  water  is  at  the  same  level  in  both  vessels. 

Temperature  is  not  heat ;  level  is  not  water ;  and  potential 
is  not  electricity,  but  merely  the  state  of  the  conductor  which 
determines  the  direction  of  transfer  of  electricity. 

All  points  of  a  conductor,  when  the  electricity  upon  it  is  at  rest, 
are  at  the  same  potential,  regardless  of  any  difference  of  density  which 
may  exist  ojt  different  points.  If  it  were  not  so  there  would  be  a 
continual  flow  of  electricity  from  the  higher  to  the  lower  until 
equilibrium  was  established,  i.e.  until  all  points  had  the  same  po- 
tential. We  can  demonstrate  this  fact  by  experiment. 

Experiment  1.  —  Charge  a  pear-shaped  body,  A  (Fig.  347),  with 
electricity.  Connect  a  proof-plane  with  an  electroscope  and  touch 
the  charged  conductor  with  the 

proof-plane  at  different  points  ;  ^-~^-— 

the  leaves  diverge  just  the  same  J^f^ 

at  all  points  touched,  thus  show-    A\^^^  Lc^  /A 

ing  that   the   potential   at   all  /  ^"^^^Q  /    \ 

points  is  the  same,  although  the  A  J^} 

density  at  different  points  varies  \       ^^—— 
(compare  this  experiment  with   ^"~~  -piG  347 

Exp.  2,  Section  III). 

Observe  that  it  is  difference  of  potential,  or  simply  potential,  and 
not  quantity  or  density,  which  determines  a  flow  of  electricity. 
Water  does  not  flow  from  a  larger  or  deeper  pond  into  a  smaller 
or  shallower  one  unless  there  is  a  difference  of  level.  , 

416.    Electrical  capacity. 

If  two  conductors  of  the  same  shape,  and  surrounded  by  the 
same  dielectric,  be  charged,  it  will  be  found  that  the  larger  one  re- 
quires a  larger  charge  than  the  smaller  one  to  electrify  it  to  the 
same  potential ;  i.e.  the  larger  one  has  a  greater  electrical  capacity 
than  the  smaller  one.  Hence  the  potential  of  a  conductor  depends 
upon  its  charge  and  its  capacity.  If  C  =  the  capacity  of  a  con- 
ductor, Q  =  the  quantity  or  charge  of  electricity,  and  V  =  the 
potential,  then  n 


452 


ETHER    DYNAMICS. 


From  this  we  see  that  the  capacity  of  a  conductor  is  equal  to  the 
charge  necessary  to  raise  its  potential  from  zero  to  unity. 

The  capacities  of  spheres  are  found  to  be  proportional  to  their 
radii.  Thus  if  a  sphere  charged  with  20  units  of  electricity,  and 
having  a  radius  of  4  inches,  be  brought  in  contact  with  an  un- 
charged sphere  having  a  radius  of  1  inch,  and  these  be  afterwards 
separated,  the  quantity  on  the  large  one  will  be  16  units ;  that  on 
the  small  one,  4  units. 


SECTION  V. 

INDUCTION.       ELECTRICAL    MACHINES. 

417.  Electr-ophorus.  —  This  apparatus   is  used  to  produce 
electrification  by  induction.     It  consists  of  a  shallow  iron 
dish,  A  (Fig.  348),  rilled  with  sealing-wax.     At  the  center 

of  the  dish  is  a  protuberance,  B,  which  ex- 
tends just  through  the  wax.  A  flat  brass 
disk,  C,  has  a  glass  insulating  handle. 

Experiment  1.  —  Strike  the  surface  of  the  wax 
a  few  times  with  a  cat's  fur,  or  rub  it  with  a  dry 
flannel.  The  wax  becomes  electrified  with  —  E. 
Place  the  disk  C  upon  it.  The  +E  of  the  disk  is 
bound  by  the  —  E  of  the  wax,  but  the  —  E  of  the 
disk  is  repelled  by  the  —  E  of  the  wax  and  passes 
through  the  protuberance  B  to  the  dish  below, 
and  thence  to  the  earth.  Consequently  when  the 
disk  C  is  raised  by  the  insulating  handle  from  the 
wax,  it  is  charged  with  +E,  and  the  charge  can 
be  transferred  to  any  body  (e.g.  a  Ley  den  jar,  see 
§  420),  and  then  the  disk  can  be  recharged  by 
replacing  it  on  the  wax.  This  may  be  repeated 
many  times  without  sensibly  decreasing  the  charge  of  —  E  on  the  wax. 

418.  Continuous  electrophorus.  —  Topler-Holtz  machine. 

Charging  by  means  of  the  electrophorus  like  that  described  above 
is  necessarily  intermittent.  The  Topler-Holtz  machine  acts  as  an 
approximately  continuous  electrophorus,  i.e.  the  act  of  charging  by 
this  machine  is  more  nearly  continuous. 


FIG.  348. 


CONTINUOUS  ELECTROPHORUS.         453 

Fig.  349  represents  this  machine  in  perspective,  and  Fig.  350  is 
a  diagram  of  its  essential  parts.  On  the  back  of  a  stationary  glass 
plate,  F  F  (Fig.  350),  called  the  field  plate,  are  pasted  two  quadrants 
of  varnished  paper,  1 1,  called  the  inductors.  In  front  of  the  field 
plate  is  a  revolving  glass  plate  upon  which  are  pasted  equidistant 
tin-foil  carriers,  aaa'  a'  n  >i',  having  a  flat  metal  button  on  the 
center  of  each.  Two  brushes  of  tinsel,  C  C,  connected  with  the 
inductors,  are  so  supported  as  to  touch  the  buttons  as  they  pass, 
and  thus  a  connection  is  established  between  the  buttons  in  tem- 
porary contact  with  the  brushes  and  the  inductors.  A  stationary 


metal  rod,  A  B,  has  metal  combs  with  pointed  tee*h  attached  to  it 
near  each  end.  The  central  teeth  of  these  combs  are  removed  and 
replaced  by  tinsel  brushes.  This  rod  serves  as  a  conductor  between 
the  two  buttons  on  the  same  diameter,  and  may  be  called  the  neu- 
tralizing conductor.  A  second  pair  of  combs,  C'  C",  are  connected 
with  the  separable  discharging  conductor  K  K'.  Connected  with 
each  part  of  this  conductor  is  a  Leyden  jar  or  condenser. 

The  mere  contact  between  unlike  substances  is  sufficient  to  pro- 
duce a  very  small  incipient  charge  which,  as  the  plate  revolves, 
rapidly  increases  to  a  maximum.  In  starting  this  action  the  two 
parts  of  the  discharging  conductor  are  usually  brought  in  contact. 
As  the  two  parts,  K  and  K',  become  oppositely  charged,  they  may  be 
separated  farther  and  farther  apart,  and  discharges  between  the  two 
extremities,  in  the  form  of  sparks  and  brushes,  occur  at  intervals, 


454 


ETHER   DYNAMICS. 


which  increase  with  an  increase  of  distance.  By  the  addition  of 
Leyden  jars,  which  also  become  oppositely  charged,  the  amount  of 
charge  previous  to  each  discharge  is  increased,  and  consequently 
the  energy  of  the  discharge  and  the  brilliancy  of  the  spark  are 
increased,  though  the  discharges  are  less  frequent. 

As  the  plate  rotates,  the  two  inductors  are  kept  constantly  and 
oppositely  charged,  and  as  two  opposite  carriers  (n  and  n'  for  ex- 
ample) are  about  to  leave  the  inductors  the  following  takes  place  : 
At  n  the  positively  charged  inductor  acts  through  the  glass  upon  the 
carrier  and  comb,  attracting  and  binding  the  — E  and  repelling  +E. 
Similar  action  takes  place  at  n',  but  with  opposite  signs.  These 


repelled  charges  unite  through  the  conductor  A  B  and  neutralize 
each  other,  leaving  the  carriers  n  and  n'  charged  respectively  with 
— E  and  4-E.  As  n  and  n'  move  away  from  the  inductors  their 
charges  become  free,  and  on  reaching  the  brushes  C  C  they  com- 
municate a  portion  of  their  charges  to  the  brushes  to  make  good 
any  losses  by  leakage  or  otherwise  which  the  inductors  may  sustain. 
We  are  now  able  to  see  how  the  charges  of  the  inductors  are  re- 
ceived and  maintained. 

We  now  turn  our  attention  to  the  discharging  conductor.  The 
two  inductors  act  inductively  upon  the  two  parts  K  and  K'  of  the 
conductor,  charging  K  with  +E  and  K'  with  —  E.  The  work  re- 


CONDENSER.  455 

quired  to  keep  up  the  motion  of  the  revolving  plate  increases  as  the 
charges  rise,  as  there  is  a  constant  pulling  apart,  at  different  points, 
of  bodies  oppositely  charged.  Thus  mechanical  energy  becomes 
transformed  into  electric  energy,  or  the  energy  of  ether  strain.1 

The  above  is  a  partial  description  of  the  action  of  this  machine. 
For  a  complete  description  the  student  may  consult  larger  works.2 

419.  Condenser.  — A  very  important  adjunct  to  an  electrical 
machine  is  a  condenser  of  some  kind,  by  means  of  which  a  large 
quantity  of  electricity  can  be  collected  on  a  small  surface. 

Experiment  2.  —  Let  a  person  stand  on  an  insulated  stool  (§  400),  and 
place  one  hand  on  the  prime  conductor  of  a  machine.  Let  the  other 
open  hand  press  against  a  plate  of  glass  or  disk  of  vulcanite,  held  on  the 
open  hand  of  a  second  person  standing  on  the  floor.  After  a  few  turns 
of  the  machine,  let  the  hand  that  has  been  on  the  prime  conductor  grasp 
the  free  hand  of  the  second  person.  Quite  a  shock  will  be  felt  by  both. 
Or  the  connection  may  be  made  through  a  group  of  persons  having  hold 
of  one  another's  hands,  when  the  whole  company  may  receive  a  shock. 

It  is  evident  that  by  this  process  an  unusual  quantity  of 
electricity  had  collected  previous  to  the  discharge.  This 
furnishes  an  excellent  illustration  of  how  electricity  may  be 
bound  by  inductive  action.  The  explanation  is  simple.  The 
hand  of  the  first  person,  charged  with  -J-  E,  acts  by  induction 
through  the  glass  upon  the  second  person,  attracting  —  E  to 
the  surface  of  the  glass  with  which  his  hand  is  in  contact, 
and  repelling  -f  E  to  the  earth.  Thus,  through  their  mutual 
attraction,  the  two  kinds  of  electricity  become,  as  it  were, 
heaped  up  opposite  each  other,  and  yet  are  prevented,  by  the 
insulating  glass,  from  uniting. 

It  thus  appears  that  the  electrical  capacity  of  a  body  depends 
not  only  upon  its  size  (§  410)  but  upon  the  presence  of  charges  upon 
other  conductors. 

1  After  a  Topler-Holtz  machine  has  charged  a  battery  of  Leyden  jars,  i.e.  stored 
up  in  the  jars  electrical  energy,  the  belt  may  be  slipped  from  the  machine  (to  reduce 
friction),  when  the  battery  will  drive  the  machine,  reconverting  the  energy  into 
mechanical  energy. 

2  Consult  Barker,  Ganot,  Cumming,  etc. 


456  ETHER    DYNAMICS. 


Since  C  =      (§  416),  it  is  evident  that  the  increase  in  capacity  of 

the  conductor  is  not  due  to  an  increase  of  potential.  An  electrical 
condenser  may  be  regarded  as  an  appliance  for  increasing  the  charge 
without  increasing  the  potential. 

420.  Leyden  jar.  —  One  of  the  most  convenient  forms  of 
condenser  is  the  Leyden  jar.1     It  consists  of  a  glass  jar  (Fig. 
351)  coated  with  tin-foil  both  inside  and  outside  to  about 
two-thirds  its  hight.     ^  brass  rod  passes  inside  through  a 

varnished  wooden  stopper,  and 
touches  the  inner  foil,  and 
terminates  in  a  brass  knob  on 
the  outside. 

The  jar  may  be  charged  by 
connecting  one  of  its  coatings 
with  the  conductor  of  an  elec- 

FlG.  351.  FIG.  352.  J     .       .  .  .  _     J  . 

trical  machine  and  the  other 

with  the  earth.  Or  it  may  be  charged  by  connecting  the 
outside  coating  with  one  of  the  discharging  conductors  of 
the  Holtz  machine,  and  bringing  the  other  pole  near  to  the 
ball  leading  from  the  inner  coating.  To  discharge  the  jar, 
connect  the  outer  coating  with  the  knob  of  the  jar.  To  avoid 
a  shock  in  so  doing,  a  discharger  is  used  (Fig.  352),  which 
consists  of  a  bent  wire  terminating  at  each  end  with  metal 
balls.  The  wire  is  held  by  a  glass  insulating  handle. 

421.  Capacity  of  a  condenser.  —  The  capacity  of  a  conden- 
ser is  proportional  (1)  to  the  area  of  the  metallic  conductor  ; 

(2)  to  the  specific  inductive  capacity  of  the  dielectric  ;  and 

(3)  is  inversely  proportional  to  the  thickness  of  the  dielectric. 

1  So  called  because  one  of  the  first  jars  was  constructed  (by  Cuneus)  at  Leyden, 
Holland  (1746).  The  original  discovery  was,  however,  made  a  year  earlier  by  Kleist 
of  Pomerania.  He  happened  to  touch  a  charged  conductor  of  an  electrical  machine 
with  a  nail  protruding  from  a  bottle  containing  water.  On  removing  the  bottle  and 
attempting  to  remove  the  nail  from  the  bottle  he  received  a  violent  shock.  His 
hand  on  the  outside  of  the  bottle  and  the  water  on  the  inside  undoubtedly  answered 
the  purpose  of  coatings. 


CONDITION    OF    THE    DIELECTIUC. 


457 


The  low  inductive  capacity  of  some  kinds  of  glass  renders  it 
entirely  unsuitable  for  this  purpose. 

To  secure  greater  capacity  than  a  single  jar  of  ordinary 
capacity  will  afford,  several  jars,  constituting  a  "  battery  "  of 
jars  (Fig.  353),  are  placed  upon  a  sheet  of  tin-foil  so  as  to 
connect  all  the  outer  coatings,  while  the  inner  coatings  are 


FIG.  353. 

connected  by  a  wire  joining  their  projecting  rods.  The  sev- 
eral jars  are  by  this  means  practically  converted  into  one 
large  jar. 

422.  Condition  of  the  dielectric.  Seat  of  charge.  —  That 
inductive  action  is  attributable  to  the  dielectric,  and  not  to 
the  conductor,  is  shown  by  the  Leyden  jar  with  movable 
coatings  (A,  Fig.  354).  B  is  the  dielectric  ;  C  is  the  outer  and 
D  the  inner  conductor.  The  several  parts  being  put  together, 
the  jar  is  charged  in  the  usual  manner  and  placed  upon  an 
insulator.  Then  the  inner  conductor,  D,  is  raised  by  a  glass 
rod  out  of  the  jar,  and  afterwards  the  glass  vessel,  B,  is 
removed  from  the  outer  coating.  The  several  parts  are  now 
tested  with  an  electroscope.  The  coatings  produce  little  or 
no  disturbance  of  the  leaves ;  the  glass  causes  a  divergence  of 


458 


ETHER    DYNAMICS. 


the  leaves.  On  putting  the  parts  together  again  and  dis- 
charging in  the  usual  way,  there  will  be  nearly  as  brilliant  a 
spark  as  if  the  charged  jar  had  not  been  dissected. 

This  experiment  demonstrates  that  (1)  the  seat  of  the 
charges  is  on  the  surface  of  the  glass  and  not  on  the  coat- 
ings ;  (2)  the  coatings  serve  merely  the  purpose  of  conductors 
to  spread  electricity  at  the  time  of  charging,  and  to  allow  its 
escape  from  all  parts  of  the  electrified  surfaces  at  the  time 


FIG.  354. 

of  discharge ;  (3)  a  charge  is  not  an  electrification  of  the 
conductors,  but,  rather,  of  the  dielectric,  or,  as  we  shall  say 
later  on,  of  the  "field"  itself,  the  extent  of  the  conductor 
determining  the  limits  of  the  field. 

423.  Limit  of  the  charge  of  condensers.  —  There  is  a  limit 
beyond  which  a  condenser  cannot  be  charged.  When  elec- 
trification takes  place,  the  stress  produced  by  the  opposite 
charges  causes  a  strain  in  the  glass.  When  the  strain  be- 
comes too  great,  a  discharge  occurs  across  the  dielectric,  either 
through  the  air  over  the  top  of  the  jar,  or,  if  the  glass  be  thin 
enough,  by  puncturing  it. 


CONTACT    ACTION.  459 

SECTION  VI. 

ELECTROSTATIC    LINES    OF    FORCE.        FIELD    OF    FORCE. 

424.  Contact  action. 

Bring  two  bodies  of  dissimilar  nature  (e.g.  a  stick  of  sealing-wax 
and  a  woolen  cloth)  in  contact,  best  by  rubbing  to  secure  better 
contact,  and  separate  them,  and  they  exhibit  strong  attraction  for 
each  other,  ordinarily  vastly  greater  than  that  of  gravitation.  The 
contact  serves  to  establish  bonds  of  attraction,  i.e.  the  ether  between 
them  is  supposed  to  operate  like  india-rubber  bands,  pulling  the  two 
bodies  together.  The  bodies  are  thus  said  to  be  electrically  excited. 
To  separate  the  excited  bodies  requires  work  to  be  done  ;  and  the 
bodies  when  separated  possess  energy  of  electrical  separation. 

425.  Lines  of  force.     Field  of  force. 

The  space  or  dielectric  between  and,  to  a  limited  extent,  around 

the  excited  bodies  is  assumed  by  Faraday  to  be  full  of  what  he 

called  lines  of  force,  the  positive  direction  of  a  line  at  any  point  in 

this  space  being  the  direction  in  which  a  positively  electrified  particle 

tends  to  move  under  the  influence  of  the  electrical  field.    The  space 

thus  occupied  by  lines  of  force  is  called  the  field  of  force.  Faraday 
remarks  that  the  stress  is  as  if  these  lines  were  stretched 
elastic  threads  endowed  with  the  property  of  shortening 
themselves  and  also  the  property  of  repelling  one  another 
as  well.  In  other  words,  there  is  a  tension  along  these  lines 
and  a  pressure  at  right  angles  to  them.  When  bodies 
oppositely  excited  are  brought  near  together,  the  lines  are 

almost  straight  from  one  to  the  other  (except  near  the  edges)  of  the 

facing  areas,  as  shown  in 

Fig.    355.      As  they   are 

more  separated  the  lines 

curve     outward,     always 

tending  to  separate  from 

one  another  and  from  the 

common  axis  of  the  two 

bodies,  some  even  curling 

round  to  the  back  of  the 

bodies,  as  represented  in 

Fig.  356.     The  expression 

' '  lines  of  force  ' '  must  be  FIG> 


460  ETHER    DYNAMICS. 

regarded  as  purely  a  matter  of  convenience.     They  have  no  more 
and  no  less  existence  than  have  "rays  of  light." 


SECTION  VII. 

ATMOSPHERIC    ELECTRICITY. 

426.  Lightning.  —  Franklin,  by  a  series  of  historic  experi- 
ments, proved  the  exact  similarity  of  lightning  and  thunder 
to  the  light  and  crackling  of  the  electric  spark.      Certain 
clouds  which  have  formed  very  rapidly  are  highly  charged, 
usually  with  -f-  E,  but  sometimes  with  —  E.     The  surface  of 
the  earth  and  objects  thereon  immediately  beneath  the  cloud 
are,  of  course,  charged  inductively  with  the  opposite  kind  of 
electricity.     The  cloud  and  the  earth  correspond  to  the  coat- 
ings, and  the  intervening  air  to  the  dielectric,  of  an  immense 
condenser.      The  opposite  charges  on  the  earth  and  on  the 
cloud  hold  each  other  prisoners  by  their  mutual  attraction. 

As  condensation  progresses  in  the  cloud  its  capacity  de- 
creases and  its  potential  rises  (since  CV  =  Q).  This  process 
continues  till  the  difference  of  potential  between  the  cloud 
and  the  earth  becomes  great  enough  to  produce  a  discharge 
through  the  air. 

It  is  the  accumulation  of  induced  charges  on  elevated 
objects,  such  as  buildings,  trees,  etc.,  that  offers  an  intensi- 
fied attraction  for  the  opposite  electricity  of  the  cloud  in 
consequence  of  their  greater  proximity,  and  renders  them 
especially  liable  to  be  struck  by  lightning. 

The  clouds  gather  electricity  from  the  atmosphere.  Our 
knowledge  of  the  method  by  which  the  atmosphere  becomes 
charged  is  very  limited. 

427.  Lightning-rods.  —  A  good  lightning  conductor  offers  a 
peaceful  means  of  communication  between  the  earth  and  a 
cloud  ;  it  leads  the  electricity  of  the  earth  gently  up  toward 


THE   AURORA.  461 

the  cloud,  and  allows  it  to  combine  with  its  opposite  without 
disturbance,  thereby  so  far  discharging  the  cloud  as  possibly 
to  prevent  a  lightning  stroke  ;  or,  if  the  stress  be  too  great  to 
be  thus  quietly  disposed  of,  the  flash  strikes  downward,  and 
is  led  harmlessly  to  the  earth  by  the  conductor.  An  ill-con- 
structed lightning-rod  may  be  worse  than  none.  A  good  rod 
should  be  made  of  good  conducting  material,  so  large  that  it 
will  not  be  melted,  and  free  from  loose  joints.  The  lower 
end  should  be  buried  in  earth  that  is  always  moist,  and  the 
upper  end  should  terminate  in  several  sharp  points.  Maxwell 
suggests  that  the  best  form  for  a  lightning  protector  is  one 
which  approximates  a  net-work  covering  the  entire  house 
(see  foot-note,  p.  445). 

428.  The  aurora  is  a  luminous  phenomenon  caused  (as 
experiments  performed  by  Lemstrom  in  Lapland  seem  to 
indicate)  by  currents  of  electricity  passing  from  the  higher 
and  rarefied  regions  of  the  atmosphere  to  the  earth.  In  the 
Arctic  regions  the  aurora  borealis  (northern  lights)  is  of 
almost  daily  occurrence.  It  sometimes  forms  an  arch,  and 
sometimes  illuminates  the  whole  sky. 

Electrical  Age,  New  York  :  Thunder  is  caused  by  the  lightning 
spark  heating  the  air  in  its  path,  causing  sudden  expansion  and 
compression  all  around,  followed  by  as  sudden  a  rush  of  air  into 
the  partial  vacuum  thus  produced.  If  the  spark  be  straight  and 
short  the  clap  will  be  short  and  sharp  ;  if  its  path  be  a  long  and 
crooked  one,  a  succession  of  sounds,  one  after  the  other,  with  a 
characteristic  rattle,  will  be  heard,  followed  by  the  echoes  from 
other  clouds.  The  echoes  have  a  rolling  and  rumbling  sound. 


462  ETHEK    DYNAMICS. 


CHAPTEE   III. 

ENERGY   OF   ELECTRIC   FLOW.     ELECTRO-KINETICS. 
SECTION  I. 

INTRODUCTORY    EXPERIMENTS. 

429.  Apparatus  required. 

There  are  required  a  condensing  electroscope,  i.e.  one  which  has  two 
disks  separated  from  each  other  by  a  dielectric  (Fig.  358),  the  upper  one 
having  an  insulating  handle ;  a  tumbler  |  full  of  water,  into  which  have 
been  poured  two  or  three  tablespoonf uls  of  strong  sulphuric  acid  ;  a  strip 
of  sheet-copper,  and  two  pieces  of  rolled  zinc,  each  about  5  inches  long, 
1|  inches  wide,  and  at  least  T3¥  of  an  inch  thick  (a  piece  of  No.  16  copper 
wire  12  inches  long  should  be  soldered  to  one  end  of  each  piece  of  metal, 
and  the  soldering  covered  with  asphaltum  paint);  2  yds.  of  silk  insulated 

No.  18  copper  wire;  two  double 
connectors  (Fig.  357)  which  serve 
to  join  two  wires  without  the  in- 
convenience of  twisting  them  to- 
FIG.  357.  gether ;  and  a  battery  of  four  vol- 

taic cells  (either  Bunsen  or  other 

reputable  kind).  One  of  the  zincs  should  be  amalgamated  as  follows  : 
First  dip  the  zinc,  with  the  exception  of  \  inch  at  the  soldered  end,  into 
the  acidulated  water ;  then  pour  mercury  over  the  wet  surface,  and 
finally  rub  the  surface,  now  wet  with  mercury,  with  a  cloth  (to  insure 
complete  amalgamation,  it  is  best  to  repeat  this  operation). 

430.  Experiments. 

Experiment  1.  —  a.  Put  the  unamalgamated  zinc  into  the  tumbler 
containing  acidulated  water.  Bubbles  of  hydrogen  gas  arise  from  the 
surface  of  the  immersed  zinc. 

b.  Remove  this  zinc  and  introduce  the  amalgamated  zinc.  No  bubbles 
(or  at  least  very  few)  arise  from  the  latter,  provided  that  the  zinc  is 
properly  amalgamated, 


LESSON    LEARNED. 


463 


c.  Put  the  copper  strip  into  the  liquid,  but  do  not  allow  the  two  metals 
or  their  wires  to  touch.     No  bubbles  arise  from  either  metal.     Connect 
the  wires  of  the  two  metals  with  a  double  connector ;  copious  bubbles 
arise  from  the  copper  strip,  but  very  few  from  the  zinc  strip.     Bubbles 
escaping  from  the  copper  make  it  appear  as  if  chemical  action  were  taking 
place  between  the  metal  and  the  liquid.     But  experience  will  teach  you 
that  the  appearance  is  deceptive,  as  you  will  find  that  in  no  case   is 
copper  consumed. 

d.  Substitute  the  unamalgamated  zinc  for  the  amalgamated ;  bubbles 
rise  abundantly  from  the  surfaces  of  both  the  zinc  and  copper. 

Lesson  learned :  An  unamalgamated  zinc  is  acted  on  by  the 
liquid  under  all  circumstances  ;  an  amalgamated  zinc  is  not 
acted  on  by  the  liquid  unless  the  copper  strip  is  also  in  the 
liquid,  and  not  then  unless  the  metals  are  connected.  If  then 
we  would  at  any  time  stop  the  action,  we  have  only  to  dis- 
connect the  metals.  It  seems  also  that  the  wire  connecting 
the  two  metals  serves  some  important  purpose  in  keeping  up 
this  action. 

Experiment  2.  —  In  this  experiment  it  will  be  necessary  to  use  metal 
plates  of  much  larger  size,  or  (which  will  prove  much  more  satisfactory) 
we  must  use  an  apparatus  somewhat  in  advance  of  our  present  knowledge, 
viz.  a  battery  (§  431)  of  (say)  four 
cells  connected  in  series  (§  482). 

a.  Connect  the  copper  to  the 
lower  disk  of  the  electroscope  (Fig. 
358)  by  an  insulated  wire,  merely 
touching  it  with  the  end  of  the 
wire,  and  the  zinc  to  the  upper 
disk.  Remove  the  wires,  and  lift 
the  top  disk  by  the  insulating  han- 
dle. The  leaves  of  the  electroscope 
diverge.  Prove  by  suitable  test  that 
the  electrification  in  the  leaves  is 

P°sitive'  FIG.  358. 

6.  Repeat    this    operation,    but 

touch  the  lower  disk  with  the  wire  from  the  zinc,  and  the  upper  one  with 
the  wire  from  the  copper.  Show  that  the  leaves  have  now  a  negative 
charge. 


464  ETHER    DYNAMICS. 

When  the  upper  plate  is  lifted,  the  capacity  of  the  condenser 
diminishes  considerably,  so  that  the  small  charge  on  the  lower  disk 
raises  its  potential  so  much  that  the  gold  leaves  diverge.  This  will 

be  understood  from  the  equation  V  =  ^  (§  416);  when  the  denomi- 

\u 

nator  C  of  the  fraction  ^  diminishes,  the  fraction  increases,  and 

O 

therefore  V  increases. 

If  a  plate  of  metal  be  placed  in  a  liquid  of  a  class  which  we 
shall  term  an  electrolyte  (i.e.  one  which  is  capable  of  being 
decomposed  by  a  current  of  electricity),  there  is  a  difference 
of  electrical  condition  produced  between  them  so  that  the 
metal  becomes  either  of  higher  or  lower  potential  than  the 
liquid,  according  to  the  nature  of  the  metal  and  liquid. 

We  know  that  if  two  conductors  be  at  different  potentials, 
electricity  tends  to  flow  from  the  one  whose  potential  is 
higher  to  that  whose  potential  is  lower  ;  if,  therefore,  two 
dissimilar  metals  be  placed  in  the  same  electrolytic  liquid 
and  we  show  by  actual  experiment,  as  above,  that  the  free 
end  of  the  wire  in  connection  with  one  plate  is  charged  with 
+  E,  and  the  free  end  of  the  other  with  — E,  we  conclude  that 
if  the  two  oppositely  charged  bodies  be  brought  in  contact,  a 
current  of  electricity  will  flow  from  the  positively  charged 
plate  to  the  negatively  charged  one.  A  current  therefore 
flows  through  the  connecting  wire  from  the  copper  (which  is 
called  the  positive  electrode}  to  the  wire  leading  from  the  zinc 
(which  is  called  the  negative  electrode),  when  they  are  con- 
nected. 

That  difference  in  quality,  in  virtue  of  which  zinc  and  cop- 
per placed  in  acidulated  water  can  give  rise  to  an  electric 
current,  is  called  their  electro-chemical  difference,  and  the  zinc 
is  said  to  be  electro-positive  to  the  copper  in  the  liquid. 
There  is  a  perplexing  nomenclature  in  use  by  which  the  zinc 
plate  is  called  the  electro-positive  element  or  plate,  though  it 
is  called  the  negative  pole  of  the  combination. 


VOLTAIC    CELL.  465 


SECTION   II.  ^ 

VOLTAIC    BATTERIES.       ELECTRIC    CIRCUITS. 

431.  Voltaic  cell.  —  Two  electro-chemically  different  solids 
(of  which  zinc  is  almost  invariably  one)  placed  in  an  electrolytic 
liquid  constitute  what  is  called  a  galvanic  or  voltaic  l  cell  (or 
pair).  One  of  these  plates  must  be  more  actively  attacked 
by  the  liquid  than  the  other ;  the  plate  most  acted  upon  is 
called  the  electro-positive  plate,  and  the  other  the  electro- 
negative one. 

The  greater  the  disparity  between  the  two  solid  elements  ivith 
reference  to  the  action  of  the  liquid  on  them,  the  greater  the 
difference  in  potential ;  hence,  the  greater  the  current. 

In  the  following  electro-chemical  series  the  substances  are  so 
arranged  that  the  most  electro-positive,  or  those  most  affected 
by  dilute  sulphuric  acid,  are  at  the  beginning,  while  those 
most  electro-negative,  or  those  least  affected  by  the  acid,  are 
at  the  end.  The  arrow  indicates  the  direction  of  the  current 
through  the  liquid. 

i  *  I  § 
+i  §  a  1  I  I  3  1- 

N      A      H      H/    O      to      fc  VO 


It  will  be  seen  that  zinc  and  platinum  are  the  two  sub- 
stances best  adapted  to  give  a  strong  current. 

When  the  wires  from  the  two  plates  are  joined  the  dis- 
charge of  the  two  plates  would  produce  electrical  equilibrium, 
were  there  not  some  means  of  maintaining  a  difference  of 
potential  between  the  two  plates.  This  is  accomplished  by 

1  The  original  Volta's  cell  consisted  of  a  plate  of  copper  and  a  plate  of  zinc  im- 
mersed in  dilute  sulphuric  acid.  It  is  a  very  inefficient  battery,  yet  with  such  an 
appliance  Sir  Humphry  Davy  performed  his  classic  experiments  upon  the  metals  of 
the  alkalis,  and  produced  the  first  voltaic  arc. 


466  ETHER    DYNAMICS. 

the  chemical  action  between  the  liquid  and  the  electro-positive 
j)late  and  at  the  expense  of  the  chemical  potential  energy  of 
the  electrolyte  and  plate.  A  voltaic  cell  is,  therefore,  a  con- 
trivance which  converts  chemical  energy  into  electrical  energy.1 
It  should  be  remembered  that  it  is  the  role  of  the  battery  to 
maintain  a  difference  of  potential  between  the  two  plates,  or 
what  is  the  same  thing,  between  the  battery  terminals  or 
poles,  and  not  to  "generate  electricity." 

432.  Circuit.  —  This  term  is   applied  to  the  entire  path 
along  which  electricity  flows,  and  it  comprises  the  battery 
itself  and  the  wire  or  other  conductor  connecting  the  bat- 
tery-plates.     Bringing  the  two  extremities   of   the  wire  in 
contact  and  separating  them  are  called,  respectively,  closing 
and  opening,  or  making  and  breaking,  the  circuit.     Opening  a 
circuit  at  any  point  and  filling  in  the  gap  with  an  instrument 
of  any  kind  so  that  the  current  is  obliged  to  traverse  it,  is 
called  introducing  the  instrument  into  the  circuit. 

433.  Ground  circuit.  —  It  was  an  early  discovery  in  tele- 
graphic history  that  a  complete  metallic  circuit  is  not  neces- 
sary, but  that,  in  common  parlance,  the  earth  can  be  used  as 
a  "return  circuit."     This  type  of  circuit  is  represented  by 
a  battery  with  a  wire  leading  from  one  plate  to  any  con- 
venient point  of  the  earth,  and  a  second  wire  leading  from 
the  other  plate  to  any  other  point  of  the  earth,  which  may  be 
many  miles  distant  from  the  first  point.     No  one  can  assert 
that  the  current  in  such  a  case  really  goes  through  the  earth 
from  one  of  these  points  to  the  other.     The  earth  may  be 
regarded  as   a  great  reservoir,  rather  than  as  a  conductor. 
The  battery  acts  like  a  pump  raising  electricity  at  one  end 
from  the  earth  and  discharging  it  at  the  other  end  to  the 
earth.     It  is  obvious  that  a  pump  might  be  kept  in  action  by 
pumping  from  an  ocean  and  back  into  the  same  ocean  with- 
out disturbing  its  level  and  yet  there  would  be  a  continuous 

1 A  single  voltaic  couple  is  usually  termed  a  cell ;  a  combination  of  cells,  a  battery. 


ELECTRO-CHEMICAL   ACTION   OF   THE   BATTERY.     467 

flow   th rough   the  water  conductors   or  pipes.     This   would 
represent  what  is  known  as  a  ground  circuit. 

434.  Theory  of  the  electro-chemical  action  of  the  battery.  — 
The  following  is  a  brief  statement  of  Grothus'  theory  of 
electrolytic  action,  somewhat  modified.  The  small  ovals  in 
Figs.  359  and  360  represent  molecules  of  the  electrolyte, 
which  in  this  case  we  suppose  to  be  water,1  each  molecule  of 
water  containing  two  atoms  of  hydrogen  (H2)  and  one  atom 


FIG.  359. 


FIG.   360. 


of  oxygen  (0).  The  series  of  molecules  a  illustrates  the 
condition  of  the  molecules  before  the  metals  are  introduced ; 
the  series  b  represents  their  condition  after  the  introduction 
of  the  metals  and  before  the  circuit  is  closed.  Fig.  360  rep- 
resents the  condition  of  things  at  the  instant  the  circuit  is 
closed  or  at  the  instant  of  discharge.  The  molecules  are 
polarized  and  like  sides  turned  in  the  same  direction.  At 
this  instant  there  is  a  redistribution  of  electricity,  an  electric 
flow,  an  equalization  of  potential.  At  this  instant,  chemi- 
cally speaking,  there  is  as  it  were  an  interchange  of  partners, 
the  0  next  the  zinc  combining  with  it  to  form  ZnO,  its  H2 

1  It  is,  perhaps  an  open  question  whether  the  water  (H2O)  or  the  acid  (H2SO4)  is 
the  real  electrolyte.    For  our  purpose  it  does  not  matter. 


468  ETHER    DYNAMICS. 

combining  with  the  0  of  the  next  molecule,  and  so  on  through 
the  whole  row  of  molecules,  until,  finally,  the  H2  appears  at 
the  surface  of  the  copper,  where  it  is  set  free.  Immediately 
following  the  discharge  and  equalization  of  potential  a  re- 
polarization  (b)  takes  place  followed  by  a  discharge  (c).  The 
discharges  follow  one  another  so  rapidly  as  to  furnish  prac- 
tically a  continuous  flow  of  electricity. 

435.  Electrolytic   conduction.  —  As    rapidly    as    ZnO    (zinc 
oxide)  is  formed  it  combines   with  the  sulphuric  acid  and 
forms  zinc  sulphate.     The  hydrogen  escapes  in  bubbles,  as 
has   been   shown,    from   the   electro  -  negative  plate.      Thus 
oxygen  keeps  disappearing  by  combination  with  the  zinc  at 
one  end  of  the  electrolyte  ;  the  hydrogen,  by  evolution  as  a 
gas,  disappears  at  the  other.     Meantime  the  molecules  keep 
exchanging  atoms,  so  that  a  constant  traveling  of  the  H  and 
0  atoms  through  the  electrolyte  is  kept   up,  each  conveying 
its.  own  peculiar  charge.     In  this  way  what  is  virtually  a 
current  traverses  the  liquid.     The  current,  however,  does  not 
traverse  the  liquid  as  it  does  a  wire,  but  electricity  is  trans- 
mitted   by    electrolytic    action.       The    electricity    flows    not 
through    but    with   the    atoms    of   matter.       It    is    conveyed 
through  the  liquid  by  a  procession  of  charged  atoms,  and  the 
process  of  transmission   is   more   nearly   that   of  convection 
than   of  conduction.     This  process   is  called  electrolytic  con- 
duction. 

SECTION    III. 

SOME    DEFECTS    OF    BATTERIES. 

436.  Importance  of  amalgamating  the  zinc.  —  All  commer- 
cial   zinc    contains    impurities,    such    as    carbon,    iron,    etc. 
Fig.  361  represents  a  zinc  element  having  on  its  surface  a 
particle  of  carbon  a,  purposely  magnified.     If  such  a  plate  be 
immersed  in  dilute  sulphuric  acid,  the  particles  of  carbon  will 


POLARIZATION    OF    THE    NEGATIVE    ELEMENT.       469 

form  with  the  zinc  numerous  voltaic  circuits,  and  a  transfer 
of  electricity  along  the  surface  will  take  place.  This  coast- 
ing trade,  as  it  were,  between  the  zinc  and  the  impurities  on 
its  surface,  diverts  so  much  from  the  regular  bat- 
tery current,  and  thereby  weakens  it.  In  addi- 
tion to  this,  it  occasions  a  great  waste  of  materials, 
because,  when  the  regular  circuit  is  broken,  this 
local  action,  as  it  is  called,  still  continues.  If 
pure  zinc  1  were  used,  no  local  action  would  occur 
at  any  time,  and  there  would  be  no  consumption  of 
material  except  when  the  circuit  was  closed.  If 
mercury  be  rubbed  over  the  surface  of  the  zinc  FIG  361 
after  the  latter  has  been  dipped  into  acid  to  clean 
its  surface,  the  mercury  dissolves  a  portion  of  the  zinc,  forming 
with  it  a  semi-liquid  amalgam,  which  covers  up  its  impurities, 
and  the  amalgamated  zinc  then  comports  itself  like  pure  zinc. 
437.  Polarization  of  the  negative  element. 

Experiment.  —  Construct  a  voltaic  cell  composed  of  dilute  sulphuric 
acid  and  plates  of  copper  and  zinc.  Introduce  into  the  circuit  a  gal- 
vanoscope  (§  447)  and  note  the  deflection  of  the  needle  when  the  circuit 
is  first  closed.  Watch  the  needle  for  a  time.  Little  by  little  this  deflec- 
tion will  decrease,  and  as  it  decreases  bubbles  of  gas  collect  on  the  copper 
plate.  This  accumulation  of  gas  is  called  "polarization'2  of  the  negative 
element  or  plate." 

We  already  understand  that  a  difference  of  potential  is  the 
indispensable  prerequisite  to  a  flow  of  electricity.  Accom- 
panying a  difference  of  potential  there  seems  to  be  something 
analogous  to  a  force  which  is  said  to  cause  the  flow  of,  or  to 
urge,  the  electricity  through  the  circuit.  The  film  of  gas  on 
the  copper  reduces  the  electro-chemical  difference  between  it 
and  the  zinc  plate,  upon  which  the  generation  of  this  force 
depends,  and  thereby  diminishes  the  efficiency  of  the  battery. 

1  Formerly  pure  zinc,  obtained  at  great  expense  by  distillation,  was  used. 

2  The  term  polarization  in  common  use  is  a  most  senseless  term  as  here  applied. 
Polarization  in  the  electrical  world  is  made  to  cover  a  multitude  of  sins. 


470 


ETHER    DYNAMICS. 


Instead  of  a  copper-zinc  pair,  we  soon  have  a  hydrogen-zinc 
pair.  A  single  fluid  battery  cannot,  therefore,  yield  a  current 
of  constant  strength  unless  some  means  is  used  to  remove  the 
hydrogen. 

To  overcome  this  defect  some  arrangement  must  be  adopted 
to  prevent  .this  deposit  of  hydrogen  upon  the  negative  ele- 
ment. The  usual  method  is  to  employ  in  addition  to  the 
dilute  sulphuric  acid,  which  we  will  term  the  exciting  liquid, 
some  other  substance  (usually  a  liquid)  which  is  a  strong 
oxidizing  agent,  i.e.  which  can  combine  with  and  remove  the 
hydrogen  as  soon  as  it  is  liberated  at  the  negative  plate  (or 
positive  pole).  A  substance  used  for  this  purpose  is  termed 
a  depolarizer.  A  mixture  of  a  solution  of  crystals  of  bi- 
chromate of  potassium  in  water  with  a  suitable  quantity  of 
dilute  sulphuric  acid,  forms  a  depolarizer  such  as  is  used  in 
the  so-called  bichromate  batteries.  Other  depolarizing  sub- 

stances  in  common  use  are  bi- 
chromate of  sodium,  nitric  acid 
(an  excellent  depolarizer  but 
very  objectionable  on  account 
of  the  corrosive  and  unwhole- 
some fumes  to  which  it  gives 
rise),  chromic  acid,  peroxide  of 
manganese,  copper  sulphate, 
etc. 

438.    Grenet  cell. 

This  is  a  bichromate  of  potassium 
battery  in  which  two  carbon  plates, 
C  C  (Fig.  362),  electrically  connected, 
and  a  zinc  plate,  Z,  suspended  be- 
tween them  by  a  brass  rod,  a,  are 
immersed  in  the  mixed  liquid  referred  to  above. 

This  combination  furnishes  a  much  more  energetic  and  constant 
current  than  would  be  furnished  if  only  dilute  sulphuric  acid  were 
used.  But  although  polarization  of  the  negative  element  is  dimin- 


FlG.  362. 


BUNSEN   CELL. 


471 


ished,  another  detrimental  action  is  substituted.  The  layer  of 
solution  next  to  the  carbon  plate  is  soon  (say  after  a  constant  use 
of  half  an  hour  to  an  hour)  deprived  of  its  active  oxidizing  powers, 
and  then  polarization  of  the  negative  plate  and  consequent  weak- 
ening of  the  current  set  in.  This  difficulty  may  be  partially 
remedied  by  occasionally  agitating  the  liquid  or  allowing  it  to  rest, 
during  which  time  the  various  portions  of  it  become  homogeneous 
by  diffusion,  and  the  liquid  near  the  carbons  becomes  more  active. 

439.    Bunsen  cell    1  & 

A  plan  generally  adopted  to  keep  the  oxidizing  liquid  away  from 
the  zinc  plate,  where  it  is  not  wanted  and  only  does  harm,  is  to 
place  the  carbon  plate  in  an  unglazed,  pojous,  earthen  cup  and  to 


FIG.  363. 


FIG.  364. 


surround  it  with  the  oxidizing  substance.  This  arrangement,  called 
a  two-fluid  cell,  is  that  adopted  by  Bunsen  (Fig.  363),  Grove,  Fuller, 
and  others. 

In  any  form  of  two-fluid  cell  yet  devised,  the  oxidizing  fluid 
sooner  or  later  diffuses  through  the  porous  cup  and  reaches  the 
zinc.  Destructive  action  on  the  zinc  then  begins,  which  amalga- 
mation cannot  prevent,  and  a  portion  of  zinc  is  uselessly  consumed 
without  effecting  anything  in  the  way  of  generation  of  electric  cur- 
rent. An  attempt  to  prevent  this  trouble  is  sometimes  made  by 
using  a  solid  depolarizer. 


472 


ETHER    DYNAMICS. 


440.    Leclanche  cell. 

There  is  a  class  of  galvanic  cells  in  which  the  negative  element 
is  protected  from  polarization  by  means  of  metallic  oxides.  Of 
these  the  best  known  is  the  Leclanche"  cell  (Fig.  364).  In  this  cell 
the  carbon  plate  C  is  contained  in  a  porous  cup  P,  and  packed 
round  with  fragments  of  gas-retort  coke  and  manganese  peroxide. 
The  manganese  compound  has  a  strong  affinity  for  the  hydrogen. 
But  the  chemical  action  of  solids  is  sluggish  and  they  quickly 
polarize  when  in  action.  They  need  periodical  rest  to  recover  their 
normal  condition.  Such  are  called  open-circuit  batteries,  since  they 
are  suited  for  work  only  on  lines  kept  open  or  disconnected  most 
of  the  time,  such  as  in  telephone  and  bell-ringing  circuits.  The 
zinc  element,  Z,  which  is  a  rod  of  zinc,  is  immersed  in  a  solution 
of  ammonium  chloride,  which  is  the  exciting  liquid. 


441.    Daniell  cell. 

Leaving  the  hydrogen-generating  batteries,  we  will  examine 
briefly  another  form  incapable  of  this  species  of  polarization.  The 
Daniell  cell  (Fig.  365)  uses  a  solution  which,  instead  of  depositing 
hydrogen,  deposits  copper  upon  a  copper 
negative  plate,  and  hence  is  free  from  hy- 
drogen polarization.  It  contains  a  copper 
negative  and  a  zinc  positive  plate.  The 
copper  plate  is  immersed  in  a  solution  of 
copper  sulphate,  the  zinc  in  a  solution  of 
zinc  sulphate  or  dilute  sulphuric  acid,  and 
a  porous  cup  separates  the  two  liquids.  By 
the  electrolytic  action,  the  zinc  combines 
with  the  sulphuric  acid  (H2S04)  forming  zinc 
sulphate  (ZnSO4),  thereby  setting  hydrogen 
free.  This  hydrogen,  while  on  its  way  to 
the  negative  element  of  the  copper  plate, 
meets  the  copper  sulphate  solution  (CuS04) 
which  it  decomposes,  forming  sulphuric  acid 
again  (H2S04),  and  setting  free  the  copper, 
which  is  deposited  on  the  copper  plate. 

In  some  copper  sulphate  batteries  the  porous  cup  is  not  employed, 
the  difference  in  the  specific  gravity  of  the  solutions  being  relied 
upon  to  keep  them  separate,  as  in  the  so-called  gravity  cell  (Fig. 


FIG.  365. 


DANIELL    CELL. 


473 


366).     This    form    of    cell    is   commonly   used   on   closed  circuits. 
The  chief  merits  of  these  cells  are  « 

the  complete  absence  of  polari- 
zation of  the  negative  plate  (con- 
sequently, the  constancy  in  the 
potential  difference  of  the  two 
elements)  and  the  uniformity  of 
current  which  is  yielded. 

The  kinds  of  cells  that  have 
been  devised  are  numberless.  The 
voltaic  battery  will  probably  long 
continue  to  be  of  scientific  inter- 
est, but  for  commercial  uses  it 
has  already  become  well-nigh  ob- 
solete, being  replaced  by  other 
cheaper  and  more  efficient  ap- 
pliances for  generating  electric 
currents,  to  be  hereafter  described. 
The  battery  must,  therefore,  com-  FIG.  366. 

mand  in  the  future  relatively  less  attention   in  our    text-books 
than  formerly. 


Questions. 

1.  a.  What  is  an  amalgamated  zinc  plate ?    b.  A  voltaic  cell  or  pair? 
c.  An  electrode  ? 

2.  a.  How  may  it  be  shown  that  a  plate  of  copper  and  a  plate  of  zinc 
become  electrified  when  placed  in  dilute  sulphuric  acid  ?     6.  Which  will 
be  positively  electrified  ?     c.  If  wires  leading  from  these  plates  be  joined, 
what  change  will  occur?      d.  What  purpose  does  the  connecting  wire 
serve  ?     e.  Why  ought  not  the  plates  of  a  voltaic  cell  to  touch  each  other  ? 
/.  Why  ought  not  the  wires  of  certain  voltaic  cells  to  touch  each  other 
when  not  in  use  ? 

3.  a.  What  do  you  understand  by  an  electric  current  ?     6.  What  is 
the  function  of  a  battery  ?     c.  With  what  propriety  is  the  zinc  plate  of  a 
voltaic  cell  called  the  positive  plate  and  the  negative  electrode  of  a  voltaic 
system  ? 

4.  How  does  electricity  pass  from  plate  to  plate  within  a  voltaic  cell  ? 

5.  a.  What  is  meant  by  local  currents  ?     6.  How  may  they  be  pre- 
vented ? 


474  ETHER   DYNAMICS. 

6.  a.  Give  an  example  of  a  counter  electromotive  force.     6.  By  what 
other  name  is  it  generally  known  ?     c.  What  harm  does  it  do  ?     d.  How 
may  it  "be  prevented  ? 

7.  If  you  have  the  two  leading  wires  of  a  battery,  and  the  battery  be 
concealed,  how  can  you  tell  which  of  the  wires  is  connected  with  the  zinc 
plate  of  the  battery  ? 


SECTION  IV. 

EFFECTS    PRODUCED    BY    THE    CURRENT. 

442.  Summary  of  effects.  —  The  several  effects  producible 
by  an  electric  current  are  as  follows  :  — 

(1)  Certain  compounds  in  solution  can  be  decomposed  by 
causing  the  current  to  pass  through  the  solution.    This  opera- 
tion is  called  electrolysis. 

(2)  A  magnetic  needle  suspended  on  a  vertical  pivot  will 
be  deflected  if  a  wire  through  which  a  current  is  flowing  be 
brought  near  and  parallel  to  it. 

(3)  If  a  wire  carrying  a  current  be  wound  round  a  rod  of1 
soft  iron,  the  iron  becomes  a  temporary  magnet ;  the  magnet 
is  called  an  electro-magnet. 

(4)  Heat  is  generated  in  a  wire  through  which  a  current 
flows. 

(5)  If  the  temperature  be  raised  sufficiently  at  any  point 
of  the  circuit,  the  conductor  at  that  point  becomes  luminous, 
as,  for  example,  in  the  production  of  the  electric  light. 

(6)  Various  physiological  effects  are  produced  by  a  current, 
such  as  "  shocks, "  a  peculiar  taste  when  the  poles  are  applied 
to  the  tongue,  the  sensation  of  light,  etc. 

The  effects  may  be  classified  as  electrolytic,  magnetic,  in- 
cluding (2)  and  (3)  ;  heating,  including  (4)  and  (5) ;  and 
physiological. 


ILLUSTRATIVE    EXPERIMENTS. 


475 


443.    Illustrative  experiments.     (1)  Electrolysis. 

Experiment  1. — Take  a  dilute  solution  of  sulphuric  acid  (1  part  by 
volume  to  20),  pour  some  of  it  into  the  funnel  (Fig.  367),  so  as  to  fill  the 
U-shaped  tube  when  the  stoppers  are  re- 
moved. Place  the  stoppers  which  support 
the  platinum  electrodes  tightly  in  the  tubes. 
Connect  with  these  electrodes  the  battery 
wires.  Instantly  bubbles  of  gas  arise  from 
both  electrodes,  accumulating  in  the  upper 
part  of  the  tube  and  forcing  the  liquid  back 
into  the  tunnel.  Close  the  passage  in  the 
rubber  tube  by  turning  down  the  screw  of 
the  pinch-cock  a.  Light  a  splinter  of  fine 
wood,  blow  out  the  flame,  leaving  it  glow- 
ing ;  remove  the  stopper  holding  the  + 
electrode  and  introduce  the  glowing  splinter 
into  the  gas  in  this  arm  of  the  tube.  It 
relights  and  burns  vigorously,  showing  that 
the  gas  is  oxygen.  Platinum  electrodes  are 
used,  otherwise  a  portion  of  the  oxygen 
carried  to  the  +  electrode  would  not  be  set 
free,  but  would  oxidize  the  metal  (e.g. 
copper),  instead  of  appearing  as  a  gas  in 
this  arm  of  the  tube.  Fill  this  arm  of  the 
tube  with  water  and  stopper  it.  Invert  the 
U-tube ;  the  gas  in  the  other  arm  of  the 
U-tube  collects  in  the  bend  of  the  tube  and 
in  the  small  branch  tube.  Light  a  match,  remove  the  rubber  tube,  and 
quickly  bring  the  match  near  the  orifice  of  the  branch  tube.  The  gas 
burns ;  it  is  hydrogen. 

If  the  experiment  be  performed  with  a  Hoffman's  voltameter1 
(Fig.  368),  the  gas  given  off  at  each  electrode  may  be  meas- 
ured by  the  graduations  on  the  arms  of  the  tube.  It  will 
be  found  that  the  volume  of  hydrogen  given  off  is  just  double 
that  of  the  oxygen  liberated  in  the  same  time.  There  is  another 
important  use  to  which  this  apparatus  is  put  worth  men- 


FlG.  367. 


1  Any  vessel  employed  for  performing  and  measuring  electrolysis  is  called  a 
voltameter. 


476 


ETHER    DYNAMICS. 


tioning  at  this  point,  though  a  little  out  of  place.  The 
quantity  of  gas  given  off  divided  by  the 
number  of  seconds  the  current  has  been 
flowing  is  a  direct  measure  of  the  mean 
strength  of  the  current,  i.e.  the  number 
of  units  of  electricity  which  flow  through 
the  circuit  in  one  second.  Hence  this 
apparatus  serves  to  measure  current 
strength. 

The  electrode  by  which  the  current  en- 
ters the  electrolyte  is  called  the  anode; 
and  that  by  which  the  current  leaves, 
the  cathode.  The  elements  into  which  the 
electrolyte  is  broken  up  are  called  the  ions. 
The  ion  appearing  at  the  anode  is  the 
anion;  and  that  at  the  cathode,  the  cation. 
444.  Relation  of  the  electrodes  and  battery  elements.  —  It 
will  be  observed  that  in  both  the  battery  and  the  voltameter 
the  hydrogen  is  lib- 
erated at  the  plate 
toward  which  the 
current  is  flowing, 
as  shown  in  the 
diagram  (Fig.  369). 
Hydrogen  and  all 
metals  appear  on 
the  plate  toward  which  the  current  flows,  whether  in  the 
decomposing  cell  or  the  battery ;  for  example,  the  silver  in 
Exp.  4  appears  at  the  cathode,  and  the  copper  in  the  Daniell 
cell  (§  441)  is  deposited  on  the  electro-negative  plate. 

Experiment  2.  —  Take  in  a  test-tube  a  quantity  of  an  infusion  of  purple 
cabbage  prepared  by  steeping  its  leaves  until  well  cooked.  Pour  into 
this  infusion  a  few  drops  of  any  alkali,  such  as  a  solution  of  caustic  soda. 
The  infusion  is  changed  thereby  from  a  purple  to  a  green  color.  In  another 


FIG.  369. 


ILLUSTRATIVE   EXPERIMENTS. 


477 


test-tube  take  another  portion  of  the  purple  infusion.     Into  this  pour  a 

few  drops  of  any  acid,  such  as  dilute  sulphuric  acid.     The  purple  is 

changed  to  a  red.     Only  acids  will  turn  this  infusion 

to  a  red  and  only  alkalies  will  turn   it  to  a  green. 

Into   a   rather  strong  solution   of  sodium  sulphate 

pour  enough   of   the   purple    infusion  to    give   it  a 

decided  color. 

Pour  some  of  this  colored  solution  into  a  V-shaped 
glass  tube  (Fig.  370).  Into  each  arm  of  the  tube  in- 
troduce a  platinum  electrode  and  join  these  to  the 
battery  wires.  Soon  the  liquid  around  the  cathode 
is  turned  green,  while  that  around  the  anode  is  turned 
red.  Evidently,  decomposition  of  the  sodium  sulphate  has  taken  place. 
An  acid  and  an  alkali  are  the  results. 

When  a  chemical  salt  is  electrolyzed,  the  base  appears  at  the 
cathode,  and  the  acid  at  the  anode. 

Experiment  3.  —  Dissolve,  by  heating,  about  three  grams  of  pulverized 
potassium  iodide  in  about  a  tablespoonful  of  water.  Make  a  paste  by 
boiling  pulverized  starch  in  water.  Take  a  portion  of  this  paste  about 


FIG.  370. 


the  size  of  a  pea,  and  stir  it  into  the  solution. 

Wet  a  piece  of  writing  paper  with  the  liquid 

thus  prepared.    Spread  the  wet  paper  smoothly  pIG  372. 

on  a  piece  of  tin,  e.g.  on  the  bottom  of  a  tin 

basin  (Fig.  371).     Press  the  negative  electrode  of  the  battery  against  an 

uncovered  part  of  the  tin.     Draw  the  positive  electrode  over  the  paper. 

A  mark  is  produced  upon  the  paper  as  if  the  electrode  were  wet  with  a 

purple  ink.     In  this  case  the  potassium  iodide  is  decomposed,  and  the 

iodide  combining  with  the  starch  forms  a  purplish  blue  compound. 

Experiment  4. — Dissolve   about  3  g.   of  silver  nitrate   in   100  cc   of 
water.     With  this   solution   nearly  fill  the  electrolysis  tank   (Fig.  372) 


478 


ETHER   DYNAMICS. 


which  accompanies  the  porte-lumiere  (§  323).      Place  the  tank  in  the 
porte-lumiere  in  position  to  be  projected  upon  a  screen  in  a  dark  room. 

Connect  the  battery  wires  with  the  elec- 
trodes in  the  tank.  A  beautiful  deposit 
of  silver  will  be  made  on  the  cathode, 
spreading  therefrom  toward  the  anode, 
and  bearing  a  strong  resemblance  to  vege- 
table growth  ;  hence  it  is  called  the  "sil- 
ver tree.*"  In  Fig.  373,  A  represents  a 
silver  tree  deposited  from  a  weak  solu- 
tion, and  B  one  from  an  extremely  weak 
solution. 

445.  (2)  Magnetic  action  and 
magnetic  field  of  a  straight  cur- 
rent. Magnetic  lines  of  force. 

Experiment  5.  —  Construct  a  low  re- 
sistance battery  of  (say)  four  cells.  Close 
the  circuit  and  dip  the  wire  into  a  little 
heap  of  filings  of  soft  iron.  On  raising 
the  wire  you  will  find  filings  adhering 
in  a  cluster  to  the  wire  (Fig.  374). 

If  a  wire  bearing  a  very  strong  current  be  passed  vertically  through 
the  center  of  a  board  on  which  have  been  sifted  some  very  fine  iron 


FIG.  373. 


FIG.  374. 

filings,  the  filings  will  arrange  them- 
selves in  circular  lines  round  the 
current-carrying  wire  (Fig.  375),  thus 
furnishing  a  graphic  representation 
of  the  magnetic  field  set  up  by  a  cur- 
rent. If  a  small  pocket  compass  be 
carried  around  and  near  the  wire,  the 
needle  will  at  every  point  take  a  position  tangent  to  these  circular  lines 


ILLUSTRATIVE    EXPERIMENTS. 


479 


of  filings,  whichever  way  the  current  passes.  If  the  current  be  reversed, 
however,  the  position  of  the  n  and  s  poles  of  the  needle  will  be  reversed. 
This  clearly  indicates  that  there  is  a  difference  of  direction  of  these 
circular  lines  according  as  the  current  flows  in  one  direction  or  in  the 
other.  These  circular  lines  represent  the  so-called  magnetic  lines  of  force 
which  occupy  a  limited  space  or  field  round  a  current-bearing  wire. 

446.    Deflection  of  the  magnetic  needle  by  a  current. 

Experiment  6.  —  a.  Place  the  apparatus  (Fig.  376)  so  that  the  mag- 
netic needle,  which  points  (nearly)  north  and  south,  shall  be  parallel  with 
the  wires  Wi  and  W2.  Introduce  the  +  electrode  of  a  battery  into 
screw-cup  T2,  and  the  —  electrode  into  screw-cup  TI,  and  pass  a  current 


FIG.  376. 

through  the  upper  wire.  At  the  instant  the  circuit  is  closed  the  needle 
swings  on  its  axis,  and  after  a  few  oscillations  comes  to  rest  in  a  position 
which  forms  an  angle  with  the  wire  bearing  the  current. 

b.  Break  the  circuit  by  removing  one  of  the  wires  from  the  screw-cup. 
The  needle,  under  the  influence  of  the  magnetic  action  of  the  earth, 
returns  to  its  original  position. 

c.  Reverse  the  current  by  inserting  the  +  electrode  of  the  battery  into 
screw-cup  TI,  and  the  —  electrode  into  screw-cup  T2.     Again  there  is  a 
deflection  of  the  needle,  but  the  direction  of  the  deflection  is  reversed ; 
that  is,  the  north-pointing  pole  (N-pole),  which  before  turned  to  the 
west,  is  now  deflected  toward  the  east. 

d.  Place  your  right  hand  above  the  wire  with  the  palm  towards  the 
wire,  and  with  the  fingers  pointing  in  the  same  direction  as  that  in  which 


480  ETHER    DYNAMICS. 

the  current  is  flowing,  and  extend  your  thumb  at  right  angles  to  the 
direction  of  the  current  (Fig.  377).  You  observe  that  your  thumb  points 
in  the  same  direction  as  the  N-pole  of  the  needle  under  the  current-bearing 
wire. 

e.  Reverse  the  current  again  (so  that  it  will  flow  northward),  place 
your  right  hand  as  before  (viz.  with  the  palm  towards  the  wire,  and  with 
the  fingers  pointing  in  the  same  direction  as  the  current) ;  your  out- 
stretched thumb  still  points  in  the  same  direction  as  the  N-pole  of  the 
needle. 

/.  Introduce  the  +  electrode  of  the  battery  into  screw-cup  T3  and  the 
—  electrode  into  screw-cup  T4  so  that  the  current  will  flow  northward 
under  the  needle.  Place  the  right  hand  as  directed  before,  except  that 
it  must  be  under  the  wire,  so  that  the  wire  shall  be  between  the  hand 


FIG.  377.  —  Right  hand  above  the  wire  ;          FIG.  378.  —  Right  hand  below  the  wire  ; 
needle  below  it.  needle  above  it. 

and  the  needle  ;  the  thumb  will  point  in  the  same  direction  as  the  N-pole 
(Fig.  378).  Reverse  the  direction  of  the  current  in  this  wire,  and  apply 
the  same  test ;  the  same  rule  holds. 

The  rule  for  determining  the  direction  of  the  deflection  of 
the  N-poles  of  a  needle  when  the  direction  of  the  current  is 
known  is  this  :  Place  the  outstretched  right  hand  over  or  under 
the  wire  so  that  the  wire  shall  be  between  the  hand  and  the 
needle,  with  the  palm  towards  the  needle,  the  fingers  pointing  in 
the  direction  of  the  current  and  the  thumb  extended  laterally  at 
right  angles  to  the  direction  of  the  current ;  then  the  extended 
thumb  will  point  in  the  direction  of  the  deflection  of  the  N-pole. 

Conversely,  the  direction  of  the  current  may  be  determined 
by  ascertaining  the  direction  of  the  deflection  it  produces,  as 
follows  :  Place  the  outstretched  right  hand  over  or  under  the 


ILLUSTRATIVE    EXPERIMENTS.  481 

wire  (always  allowing  the  wire  to  come  between  the  hand  and 
the  needle)  with  the  palm  toward  the  needle  and  the  extended 
thumb  in  the  same  direction  as  the  N-pole  of  the  needle  is 
deflected;  then  the  fingers  will  point  in  the  direction  the 
current  is  flowing. 

It  will  be  observed  that  a  deflection  is  reversed  either  by 
reversing  the  current  or  by  changing  the  relative  positions  of 
the  wire  and  needle,  e.g.  by  carrying  the  needle  from  above 
the  wire  to  a  position  below  it. 

The  force  exerted  by  the  current  upon  the  needle  in  deflect- 
ing it  is  called  an  electro-magnetic  force. 
-    447.    Simple  galvanoscope  or  current  detector. 

Experiment  7.  —  Introduce  the  +  electrode  of  the  battery  into  screw- 
cup  T2  (Fig.  376)  and  the  —  electrode  into  screw-cup  TS,  so  that  the 
current  will  pass  above  the  wire  in  one  direction  and  below  it  in  the 
opposite  direction,  as  indicated  by  the  arrows.  A  larger  deflection  is 
obtained  than  when  the  current  passes  the  needle  only  once. 

If  the  right-hand  test  be  applied  it  will  be  seen  that  the 
tendency  of  the  current,  both  when  passing  the  needle  in  one 
direction  above  and  in  the  opposite  direction  below,  is  to 
produce  a  deflection  in  the  same  direction,  and  consequently 
the  two  parts  of  the  current  assist  each  other  in  producing  a 
greater  deflection. 

If  a  more  sensitive  instrument,  i.e.  one  which  will  produce 
considerable  deflections  with  weak  currents,  be  required,  then 
it  will  be  necessary  to  pass  the  current  through  an  insulated 
wire  wound  many  times  around  the  needle,  as  shown  in  the 
i  sectional  elevation  and  plan  (Fig.  379).  Such  an  instrument 
is  called  a  galvanoscope  or  current  detector,  since  one  of  its 
important  uses  is  to  detect  the  presence  of  a  current.  A 
graduated  card  divided  off  like  that  of  the  mariner's  compass 
is  placed  beneath  the  needle  so  that  the  number  of  degrees 
of  deflection  may  be  read  from  it.  Fig.  380  represents  a 


482 


ETHER    DYNAMICS. 


portable  detector  used  by  telegraph  and  telephone  line-men 
to  detect  whether  a  circuit  is  complete,  to  locate  faults,  etc. 
From  the  number  of  degrees  of  deflection  an  approximate 


GALVANOMETER  COIL 


FIG.  380. 


idea  of  the  strength  of  the  current  is  obtained.  The  magnetic 
needle  is  inside  the  box,  that  outside  being  merely  an  indicator 
attached  to  the  same  pivot. 

448.  (3)  Magnetizing  effect  of  an  electric  current.  Electro- 
magnets. 

Experiment  8.  —  a.  Wind  an  insulated  copper  wire  in  the  form  of  a 
spiral  round  a  rod  of  soft  iron  (Fig.  381).  Pass  a  current  of  electricity 
through  the  spiral,  and  hold  an  iron  nail  near  the  end  of  the  rod. 
Observe,  from  its  attraction  for  the  nail,  that  the  rod  is  magnetized. 
A  magnet  may  be  provisionally  defined  as  a  body  which  attracts  iron. 

6.  Break  the  circuit ;  the  rod  loses  its  magnetism  and  the  nail  drops. 

The  iron  rod  is  called  a  core,  the  coil  of  wire  a  helix,  and 
both  together  are  called  an  electro-magnet.  In  order  to  take 
advantage  of  the  attraction  of  both  ends  or  poles  of  the 
magnet,  the  rod  is  most  frequently  bent  into  a  U-shape 
(A,  Fig.  382).  More  frequently  two  iron  rods  are  used, 


ILLUSTRATIVE    EXPERIMENTS.  483 

connected  by  a  rectangular  piece  of  iron,  as  a  in  B  of  Fig. 
382.  The  method  of  winding  is  such  that  if  the  iron  core  of 
the  U-magnet  were  straightened,  or  the  two 
spools  were  placed  together  end  to  end,  one 
would  appear  as  a  continuation  of  the  other. 
A  piece  of  soft  iron,  b,  placed  across  the  ends 
and  attracted  by  them  is  called  an  armature. 
The  piece  of  iron  a  is  called  a  yoke. 

449.  (4)  (5)  Heating  and  luminous  effects 
of  the  electric  current.  —  Construct  a  low  re- 
sistance battery  (§  481)  of  four  to  six  cells, 
and  introduce  into  the  circuit  a  platinum 
wire,  No.  30,  about  j-  inch  long.  The  wire 
very  quickly  becomes  white  hot,  i.e.  it  emits 
white  light,  which  indicates  a  temperature 
of  approximately  1900°  C. 

This  experiment  illustrates  the  conversion  of  the  energy  of 
an  electric  current  into  heat  energy.     In  this  case  the  energy 

of  the  current  is  said  to  be 
consumed  in  overcoming  the 
™  _  resistance  which  the  con- 
ductor or  the  circuit  offers 
to  its  passage.  Heat  is  de- 
veloped by  a  current  in  every 

part  of  the  circuit,  because  all  substances  offer  some  resist- 
ance to  a  current;  in  other  words,  there  are  no  perfect 
conductors.  The  small  platinum  wire  offers  much  greater 
resistance  than  an  equal  length  of  a  larger  copper  wire  ; 
whence  the  greater  quantity  of  heat  generated  in  this  part 
of  the  circuit.  All  of  the  energy  of  any  electric  current  that 
is  not  consumed  in  doing  other  kinds  of  work  is  changed  into 
heat. 

Fig.  383  represents  a  calorimeter  of  simple  construction.     An 
inverted  wide-mouthed  bottle  has  its  stopper  pierced  by  two  stout 


484 


ETHER    DYNAMICS. 


copper  wires,  which  are  united  within  the  bottle  by  a  coil  of  fine 

platinum  wire.     Through  a  hole  bored  in  the  bottom  of  the  bottle  is 

introduced  a  thermometer,  T.  The 
bottle  contains  a  known  quantity  of 
water.  Now  if  a  current  be  passed 
through  the  coil  during  a  given  time, 
it  is  clear  that  the  amount  of  heat 
generated  can  easily  be  determined 
by  multiplying  the  known  mass  of 
water  by  its  temperature  change,  as 
indicated  by  the  thermometer.  This 
heat,  however,  is  equivalent  to  a 
definite  quantity  of  electric  energy 
transformed  in  the  wire. 

By  means  of  apparatus  of  this 
kind  Joule's  law  was  established : 
viz.  The  number  of  units  of  heat  gen- 
erated in  a  conductor  varies  as  (I)  its 

resistance,  (2)  the  square  of  the  strength  of  the  current,  and  (3)  the 

time  the  current  flows. 

450.    (6)  Physiological  effects. 

Experiment  9.  —  Place  the  copper  electrodes  of  a  single  voltaic  cell  on 
each  side  of  the  tip  of  the  tongue.  A  slight  stinging  (not  painful)  sensa- 
tion is  felt,  followed  by  a  peculiar  acrid  taste. 


FIG.  383. 


SECTION  V. 


ELECTRICAL    QUANTITIES    AND    UNITS. 

451.  Importance  of  electrical  measurements. — Less  than 
half  a  century  ago  the  experimental  sciences  of  electricity 
and  magnetism  were  in  a  great  measure  collections  of  iso- 
lated qualitative  results.  Now,  happily,  all  this  has  been 
changed.  The  introduction  of  the  absolute  system  of  units 
has  been  largely  instrumental  in  changing  experimental  elec- 
tricity and  magnetism  into  sciences  of  which  the  most  delicate 
and  exact  measurement  is  the  very  essence. 


STRENGTH    OF    CURRENT.  485 

The  wonderful  developments  which  have  been  made  in 
recent  years  in  electrical  science,  and  which  have  led  to  the 
employment  of  electric  energy  in  connection  with  a  great 
diversity  of  industrial  arts,  are  almost  wholly  due  to  a  better 
understanding  of  what  electrical  measurements  can  be  made, 
and  how  to  make  them.  Indeed,  little  of  a  practical  nature 
can  be  done  without  some  acquaintance  with  the  methods  of 
making  these  measurements. 

452.  Strength  of  current. — The  expression  strength  of  cur- 
rent means  the  rate  of  flow  of  electricity.  The  "  size  "  of  a 
stream  of  water,  or  the  "  rate  of  flow  "  might  be  indicated  by 
stating  the  number  of  gallons  which  flow  past  a  given  point 
in  a  minute.  We  have  not  adopted  in  hydraulics  any  par- 
ticular name  for  a  gallon  a  minute,  but  there  is  a  necessity  in 
electricity  for  a  term  to  denote  the  corresponding  idea  ;  in 
other  words,  there  is  a  necessity  for  a  unit  for  measuring- 
rate  of  flow  or  current  strength. 

The  so-called  C.G.S.  electro-magnetic  unit1  of  current  strength 
is  determined  as  follows  :  (First  it  is  necessary  to  define  a  mag- 
netic pole  of  unit  strength.  If  a  long  thin  magnet  be  broken  in 
the  middle,  the  broken  ends  develop  two  opposite  poles  of  equal 
strength.  Suppose  these  poles  to  be  placed  one  centimeter  apart 
and  the  attraction  between  them  to  be  measured  by  a  very  delicate 
spring  balance.  If  these  poles  are  of  such  strength  that  at  a  dis- 
tance of  one  centimeter  they  attract  each  other  with  a  force  of  one 
dyne,  they  are  said  to  be  of  unit  strength.) 

Suppose  that  a  thin  wire  is  bent  into  a  circle  of  1  cm  radius  (Fig. 
384),  and  a  magnetic  pole  of  unit  strength  is  held  at  its  center.  As 
we  shall  see  further  on,  there  is  a  force  tending  to  move  the  mag- 
netic pole  along  the  lines  of  force  of  the  magnetic  field  developed 
by  the  current,  i.e.  in  a  direction  at  right  angles  to  the  plane  of 
the  circle.  Let  this  force  be  measured  in  dynes,  which  can  be 

!The  units  which  we  are  here  discussing  are  called  electro-magnetic  units  to 
distinguish  them  from  units  of  'a  different  nature  called  electrostatic  units  (see 
Section  VI),  which  are  derived  from  the  effects  of  electrostatic  attraction  and  repul- 
sion. The  electrostatic  units  are  chiefly  used  in  connection  with  electrostatics,  and 
the  electro-magnetic  units  in  connection  with  electrodynamics.  Of  the  electro- 
magnetic units  there  are  two  systems,  the  C.G.S.  and  the  practical. 


486 


ETHER    DYNAMICS. 


done  by  weighing  in  grams  and  multiplying  the  number  of  grams 
by  980  (the  value  of  g).  Then  since  the  length  of  the  circular 
current  is  2?rcm,  the  attraction  of  a  unit  length 
of  it  is  obtained  by  dividing  the  total  force  in 
dynes  by  2?r.  If  now  there  be  passed  through 
the  wire  a  current  of  such  a  strength  that  this 
force  per  unit  of  length  is  equal  to  one  dyne,  the 
current  is  called  a  unit  current. 

A  C.G.S.  electro-magnetic  unit  of  cur- 
rent strength  is  denned  to  be  the  strength 
of  a  current  such  that  a  centimeter  of  it  acts 
on  a  unit  magnetic  pole  with  a  force  of  one 
dyne,  every  point  of  the  current  being  at  a 
distance  of  one  centimeter  from  the  pole. 

We  have  found  in  dynamics  that,  in 
practical  work,  the  C.G.S.  units  are  seldom 
used  on  account  of  their  inconvenient  size. 
The  same  applies  to  electricity.  For  prac- 
tical use  there  was  adopted  by  a  Congress 
of  Electricians  a  class  of  units  called  the  practical  units,  which 
are  certain  multiples  or  submultiples  J  of  the  C.G.S.  units. 

The  practical  unit  of  current  strength,  called  the  ampere,  is 
one-tenth  of  the  C.G.S.  unit.  The  quantity  of  electricity 
conveyed  per  second  by  a  current  whose  strength  is  one 
ampere  is  called  one  coulomb.  The  coulomb  is  the  practical 
unit  of  quantity  of  electricity. 

453.  Electro-motive  force.  The  volt.  —  Water  flows  from 
one  place  to  another  in  virtue  of  a  difference  of  pressure  be- 
.tween  the  two  places,  and  the  flow  takes  place  from  the  place 
of  high  pressure  to  the  place  of  low  pressure.  For  instance, 
when  water  flows  from  a  reservoir  or  cistern  the  pressure  at 
any  point  in  the  pipe  is  due  to  the  "  head  "  of  water  above  it. 

1  These  practical  units  are  derived  from  the  C.G.S.  electro-magnetic  ones  by 
adopting  a  new  unit  of  length,  the  earth's  quadrant  (109cm),  and  a  new  unit  of 
mass,  10— n  g,  the  second  being  retained  as  a  unit  of  time. 


FIG.  384. 


ELECTRO-MOTIVE    FORCE.  487 

If  it  be  set  flowing  by  a  force  pump,  we  might  say  the  flow  of 
water  was  due  to  a  water-motive  force  which  could  be  ex- 
pressed as  equal  to  a  "  head  "  of  a  certain  number  of  feet  of 
water. 

Similarly,  electricity  flows  in  a  conductor  only  when  there 
is  a  difference  of  what  may  be  termed  electrical  pressure  be- 
tween its  ends.  If  such  be  maintained  between  two  points 
connected  by  a  conductor,  it  obviously  represents  a  kind  of 
current-producing  force,  one  which  can  keep  electricity  in 
motion  against  resistance.  It  is  for  this  reason  called  electro- 
motive force  (E.M.F.).  Electro-motive  force  is  that  which 
maintains  or  tends  to  maintain  a  current  of  electricity  through 
a  conductor.  That  which  hinders  the  current  is  called  re- 
sistance. 

Difference  in  electrical  pressure  we  have  hitherto  assumed 
to  be  due  to  difference  of  potential.  It  is  this  difference  of 
electrical  pressure  which  sets  up  a  current  in  the  conductor. 
Potential  difference  may  be  due  to  contact  of  dissimilar  sub- 
stances, as  in  the  voltaic  cell,  or  to  the  movement  of  a  part 
of  the  conductor  in  a  magnetic  field,  as  in  the  dynamo  (§  525). 

Experience  shows  that  if  electricity  be  made  to  move*  in  oppo- 
sition to  E.M.F.,  or,  to  speak  figuratively,  be  carried  up  hill, 
such  a  displacement  of  electricity  against  electrical  stress  requires 
an  expenditure  of  energy  ;  that  is,  it  cannot  be  done  without  doing 
work  and  drawing  upon  a  supply  of  energy  of  some  form.  Dif- 
ference of  potential  is  therefore  measured  by  the  work  done  in  con- 
veying a  unit  of  electricity  in  opposition  to  E.M.F.  The  C.G.S. 
unit  difference  of  potential  is  said  to  exist  between  two  points  where 
one  erg  of  work  must  be  done  in  conveying  a  C.G.S.  unit  of  elec- 
tricity from  one  point  to  the  other. 

The  volt  is  the  name  chosen  for  the  practical  unit  of  E.M.F. 
and  difference  of  potential,  and  this  unit  is  equal  to  108 
C.G.S.  units.  For  purposes  where  great  accuracy  is  not 
required,  it  will  answer  to  consider  a  volt  as  the  E.M.F.  of 
a  Daniell's  cell ;  i.e.  it  is  about  the  difference  of  potential  be- 


488  ETHER    DYNAMICS. 

tween   the    zinc   and  copper  of   this    cell,    the  E.M.F.  of  a 
standard  Daniell  cell  being  approximately  1.07  volts. 

454.  Electrical  ivork  and  electrical  activity.      The  joule  and 
watt.  —  The  volt  is  of  such  a  magnitude  that  one  coulomb  of 
electricity  conveyed  against  an  E.M.F.  of  one  volt  requires 
an  expenditure  of  one  joule  —  one  volt-coulomb  of  energy.    The 
volt-coulomb  is  analogous  to  the  foot-pound  and  kilogram- 
meter.     Hence  if  a  coulomb  of  electricity  flow  between  two 
points  in  a  conductor  whose  difference  of  potential  is  one 
volt,  then  one  joule  of  work  is  done  thereby. 

If  a  conductor  be  traversed  by  a  current  of  one  ampere,  i.e. 
a  coulomb  per  second,  and  we  find  two  points  whose  difference 
of  electrical  level  is  one  volt,  then  the  rate  at  which  work  is 
being  done  in  that  portion  is  one  watt  =  one  joule  per  second. 
The  joule  and  watt  are  units  of  electrical  work  and  electrical 
activity,  respectively. 

455.  Resistance.      The  ohm. 

In  every  case  in  which  a  steady  electric  current  flows  in  a  con- 
ductor, it  is  found  that  if  the  difference  in  potential  between  any 
two  points  in  the  conductor  be  measured  in  volts,  and  this  number 
be  divided  by  the  strength  of  the  current  in  amperes,  a  quotient 
is  obtained  which  has  a  constant  value.  That  is,  if  the  difference 
of  potential  be  doubled,  the  flow  will  be  doubled,  and  so  on.  This 
constant  ratio  of  electric  pressure  to  electric  flow  is  called  the 
electrical  resistance  of  the  conductor  ;  that  is, 

resistance  =  pressure  -r  flow. 

If  pressure  be  measured  in  volts,  and  flow  in  amperes,  the  resist- 
ance of  a  conductor  in  which  a  difference  of  pressure  of  one  volt 
produces  a  flow  of  one  ampere  is  called  one  o^m,1  and  we  have 

1  SUMMARY  OF  PRACTICAL  ELECTRICAL  UNITS. 

Names  embalmed  in  scientific  nomenclature. 

English.  French.  German.  Italian.        American. 

James  Watt.  Charles  A.  Coulomb.          G.  S.  Ohm.  A.  Volta.        J.  Henry. 

James  P.  Joule.        Andre  M.  Ampere. 

Names  of  units  called  after  the  above. 

Power,  the  watt.       Quantity,  the  coulomb.    Resistance,  the  ohm.        Self -induction, 
Work,  the  joule.       Current,  the  ampere.         Pressure,  the  volt.  the  henry. 


RESISTANCE.  489 

pressure  in  volts  -f-  flow  in  amperes  =  resistance  in  ohms ; 

or,  divide  the  difference  in  potential  between  any  two  points  by  the 
strength  of  the  current,  and  the  quotient  is  the  resistance  between 
those  two  points  in  ohms.  Hence  resistance  may  be  denned  as  the 
ratio  of  the  E.M.F.  to  the  current  strength. 

The  unit  of  resistance  is  called  the  ohm.  Every  substance 
offers  resistance  to  the  passage  of  a  current.  Those  sub- 
stances which  offer  an  immensely  powerful  barrier  are  called 
insulators.  Yet  all  substances  conduct  to  some  extent ;  and 
when  an  insulator  is  spoken  of  the  term  is  only  relative. 

The  ohm,1  as  defined  by  the  Paris  Congress  of  Electricians 
(1884),  is  the  resistance  offered  by  a  column  of  pure  mercury  at 
0°  C.)  1  square  millimeter  in  section  and  106  centimeters  long.2 
It  is  about  the  resistance  of  9.3  feet  of  No.  30  (American 
gauge)  copper  wire  (.01  in.  diam.)  at  ordinary  temperature. 

The  dimensional  equation  for  quantity  of  electricity  is 
(Q)  =  [M*L*]. 

1  A  megohm  is  one  million  ohms.    A  microhm  is  one  millionth  of  an  ohm. 

2  In  July,  1894,  an  act  of  U.  S.  Congress  was  passed  "  To  define  and  establish  the 
units  of  electrical  measure."    The  following  are  quotations  from  this  act.    "  The 
unit  of  resistance,  known  as  the  international  ohm,  shall  be  represented  by  the 
resistance  offered  to  an  unvarying  electric  current  by  a  column  of  mercury  at  the 
temperature  of  melting  ice,  fourteen  and  four  thousand  five  hundred  and  twenty-one 
ten  thousandths  grams  in  mass,  of  a  constant  cross-sectional  area,  and  of  the  length 
of  one  hundred  and  six  and  three-tenths  centimeters." 

"  The  unit  of  current  shall  be  known  as  the  international  ampere  and  is  the 
practical  equivalent  of  the  unvarying  current,  which,  when  passed  through  a  solu- 
tion of  nitrate  of  silver  in  water  in  accordance  with  standard  specifications,  deposits 
silver  at  the  rate  of  one  thousand  one  hundred  and  eighteen  millionths  of  a  gram 
per  second." 

The  international  volt  "Is  the  electro-motive  force  that,  steadily  applied  to  a 
conductor  whose  resistance  is  one  international  ohm,  will  produce  a  current  of  an 
international  ampere." 

The  international  coulomb  "  Is  the  quantity  of  electricity  transferred  by  a  cur- 
rent of  one  international  ampere  in  one  second." 

The  international  "  Unit  of  work  shall  be  the  Joule,  which  is  practically  equiv- 
alent to  the  energy  expended  in  one  second  by  an  international  ampere  in  an  inter- 
national ohm." 

The  international  unit  of  activity  "  Shall  be  the  Watt,  which  is  practically  equiv- 
alent to  the  work  done  at  the  rate  of  one  Joule  per  second." 


490  ETHER    DYNAMICS. 

The  dimensional  equation  for  current  strength  is 

(C)=  [M'L*T-i]. 
The  dimensional  equation  for  electric  potential  or  E.M.F.  is 

(V)=  [M*L*T-2]. 

The  dimensional  equation  for  resistance  is 
(B)  -  [LT-i]. 

456.  Ohm's  Law.  —  The  three  factors,  current  (C),  electro- 
motive force   (E),    and  resistance   (R),  are  evidently  inter- 
dependent.    Their  relations  to  one  another  are  stated  in  the 
well-known   Ohm's  Law  thus  :    The  current   is  equal   to  the 
electro-motive  force  divided  by  the  resistance ;   or 

c-E- 

=B 

Hence  the  strength  of  a  current  is  directly  proportional  to 
the  E.M.F.  and  inversely  proportional  to  the  resistance. 
This  famous  law  is  at  the  base  of  a  large  portion  of  electrical 
measurements,  and  its  applications  are  developed  in  treatises 
on  the  mathematics  of  the  subject. 

457.  Resume. — The  ampere  is  analogous  to  the  "miner's 
inch"  used  by  miners  and  irrigators  in  the  Western  States. 
The  latter  denotes  the  rate  of  flow  of  water  which,  under  a 
head  of  six  inches,  will  pass  through  a  hole  one  inch  square 
in  a  board  two  inches  thick.     Let  this  head  of  water  represent 
a  volt,  and  the  resistance  of  the  hole  one  ohm;  then  the 
miner's  inch  would  represent  a  current  of  one  ampere.     The 
expression  "one  miner's  inch  per  second "  is  redundant;  so 
is  the  expression  "  one  ampere  per  second." 

A  unit  current  is  a  current  maintained  by  a  unit  E.M.F. 
against  a  unit  resistance. 

A  unit  E.M.F.  is  the  E.M.F.  required  to  maintain  a  unit 
current  against  a  unit  resistance.  A  conductor  has  a  unit 
resistance  when  a  unit  E.M.F.  or  a  unit  difference  of  poten- 


ELECTROSTATIC    UNITS.  491 

tial   between   its   two   ends  causes  a  unit   current   to   pass 
through  it. 

The  ampere  =  lO"1  C.G.S.  units  of  current. 

The  volt        =  108          u  «       E.M.F. 

The  ohm       —  109          "  u       resistance. 

From  the  numerical  values  given  above  it  will  be  seen  that  if  we 
have  a  circuit  in  which  the  resistance  is  one  ohm  and  the  E.M.F. 
one  volt,  then  the  strength  of  the  current  will  be  one  ampere  ;  for 


109 


SECTION   VI. 

ELECTROSTATIC    UNITS. 

Reference  has  been  made  in  the  foregoing  pages  to  various  elec- 
trical quantities,  and  we  give  below  definitions  of  certain  electro- 
static units,  rather  as  a  convenience  to  the  student  for  reference 
than  for  practical  use  in  connection  with  this  work. 

The  electrostatic  units  embrace  the  units  of  quantity,  potential, 
and  capacity.  No  names  have  yet  been  adopted  for  these  units. 

458.  Unit  of  quantity. 

One  absolute  unit  of  electricity  is  that  charge  on  a  very  small 
body  which,  if  placed  at  a  distance  of  one  centimeter  from  an  equal 
charge,  will  exert  through  air  a  force  of  one  dyne. 

We  can  express  the  force  between  two  quantities  q  and  q'  con- 
densed in  points  d  cm  apart  ty^fr*  (Compare  with  the  law  of 
gravitation,  §  96.)  The  dimensional  is  q  =  [M'L^T-1]. 

459.  Unit  difference  of  potential. 

Since  potential  represents  work  done  on  a  unit  of  electricity,  a 
unit  difference  of  potential  may  be  denned  as  such  a  difference 
of  potential  between  two  points  as  requires  the  expenditure  of  one 
erg  of  work  to  transfer  a  +  unit  of  electricity  from  one  point  to 
the  other,  that  point  being  at  higher  potential  to  which  the  +  unit  is 
carried.  The  dimensional  of  difference  of  potential  is  v  =  M*  L*  T-1. 


492  ETHER    DYNAMICS. 

460.  Unit  of  capacity. 

Since  capacity  is  quantity  per  unit  potential,  a  unit  of  capacity 
is  defined  as  such  a  capacity  of  a  conductor  as  requires  a  Charge  of 
one  unit  of  electricity  to  raise  it  to  unit  of  potential.  Capacity, 

c,  is  measured  by  -,  and  its  dimensional  is  c  =  L. 

461.  Electric  force  and  intensity  of  electric  field  at  a  point. 

The  electric  force  at  any  point  in  an  electric  field  or  the  intensity 
of  an  electric  field  at  any  point  is  the  force  with  which  a  unit  of 
+  E  would  be  acted  on  if  placed  at  that  point.  Its  dimensional,  /, 
is/=  [MLT-2]  -!-  [M*L*T-i],  or  [M*L~*T-i]. 

462.  Specific  inductive  capacity. 

The  specific  inductive  capacity  of  a  dielectric  is  the  ratio  of  the 
capacity  of  a  condenser,  the  space  between  the  plates  of  which  is 
filled  with  the  dielectric,  to  the  capacity  of  a  precisely  similar  con- 
denser with  air  as  a  dielectric.  It  is  therefore  simply  a  numerical 
coefficient. 

SECTION  VII. 

RULES    RELATING    TO    AN    ELECTRIC    CURRENT. 

463.  Activity  of  a  current.  —  The  unit  of  electric  activity 
(or  rate  of  doing  work)  is  the  watt.     A  watt  is  the  activity  of 
a  current  of  one  ampere  maintained  by  a  difference  of  poten- 
tial of  one  volt.     1  volt  X  1  ampere  =  1  volt-ampere  or  watt. 
Hence 

(1).    A  (watts)  =  C  (amperes)  X  E  (volts). 

(2).    The  watt  =2=  (1Q-1  X  10s  =)   107  ergs  per  second,  or 

1  CE 

-  horse-power.     Hence =  activity  in  horse-power. 

746  746 

For  example,  to  find  the  rate  at  which  energy  is  trans- 
formed in  an  electric  lamp,  measure  the  whole  current  in  am- 
peres ;  measure  the  difference  of  potential  (with  a  voltmeter) 
between  the  terminals  of  the  lamp,  in  volts ;  multiply  together 


ACTIVITY    OP   A    CURRENT.  493 

the  quantities  thus  obtained  and  divide  by  746 ;  the  result 
will  be  the  horse-power  absorbed  in  the  lamp.  That  is,  a 
current  of  C  amperes  falling  E  volts  will  perform,  in  passing 

f^TT 

through  the  instrument,  work  at  the  rate  of horse-power. 

746 

a.  Substituting  in  equation  (1)  the  value  of  C  as  given  in 

T^l  Tf2 

Ohm's  formula,  C— — ,  we  have,  A——  ;  i.e.    the    activity    is 

Ii  R 

equal  to  the  square  of  the  E.M.F.  divided  by  the  resistance. 

b.  E  =  CR  (Ohm's  formula).     If  this  value  of  E  be  substi- 
tuted, formula  (1)  becomes  A  =  C2R  ;  i.e.  the  activity  is  di- 
rectly proportional  both  to  the  square  of  the  current  strength 
when  R  is  constant  and  to  the  resistance  when  E  is  constant. 

(3).  The  amount  of  chemical  decomposition  produced  by  a 
current  in  a  given  time  varies  as  the  strength  of  the  current. 
On  this  principle  is  constructed  the  voltameter,  which  measures 
the  strength  of  a  current  by  the  amount  of  chemical  action  it 
effects  in  a  given  time. 

(4).  The  mass  in  grams  of  an  element  deposited  by  elec- 
trolysis is  found  by  multiplying  its  electro-chemical  equivalent 
(i.e.  the  mass  in  grams  of  the  element  deposited  by  one  am- 
pere in  one  second)  by  the  strength  of  the  current  in  amperes, 
and  this  product  by  the  time  in  seconds  during  which  the  cur- 
rent electrolyses. 

(5).  The  number  of  units  of  heat  developed  in  a  conductor  is 
proportional  (1)  to  its  resistance,  (2)  to  the  square  of  the  strength 
of  the  current,  and  (3)  to  the  time  the  current  is  flowing. 

A  current  of  one  ampere  flowing  through  a  resistance  of 
one  ohm  develops  therein  0.00024  calorie  of  heat  per  second. 
Hence  H  (calories)  —  C2  (amperes)  X  ft  (ohms)  X  t  (seconds) 
X  0.00024. 

Whenever  the  current  heats  a  wire,  produces  decomposition, 
or  performs  work  of  any  kind,  each  of  these  acts  is  accom- 
plished at  the  expense  of  the  potential  energy  in  the  battery. 


494  ETHER    DYNAMICS. 

If  the  current  operate  an  electric  motor  which  pumps  water, 
or  lift  a  hammer,  the  battery  loses  energy  proportional  to  the 
work  required  for  each  of  these  mechanical  acts. 

SECTION  VIII. 

INSTRUMENTS    FOR    ELECTRICAL    MEASUREMENTS. 

Our  attention  is  next  directed  to  the  consideration  of  in- 
struments for  measuring  the  quantities  which,  we  have  seen, 
are  required  to  be  known.  First  we  consider  the  instrument 
for  measuring  quantity  of  electricity,  properly  called  a  coulomb- 
meter. 

464.  Coulomb-meter.  Voltameter.  —  The  simplest  quantity- 
meter  is  based  on  the  electrolytic  effect  of  the  current,  and  is 
called  a  voltameter.  If,  for  instance,  using  the  Hoffman  vol- 
tameter (Fig.  368),  we  measure  the  hydrogen  generated  during 
a  given  time,  the  mass  or  volume  of  this  hydrogen  under  con- 
stant pressure  and  temperature  is  exactly  proportional  to  the 
number  of  coulombs  of  electricity  which  have  passed  through 
the  liquid.  The  mass  in  grams  of  any  constituent  of  an  elec- 
trolyte liberated  by  the  passage  of  one  coulomb  of  electricity, 
is  called  its  electro-chemical  equivalent.  For  commercial  pur- 
poses, instead  of  the  coulomb  as  the  unit  of  quantity,  a  larger 
unit,  the  ampere-hour  (=3600  coulombs),  is  frequently  used. 

The  following  are  the  electro-chemical  equivalents  x  per 
coulomb  and  per  ampere-hour  for  a  few  metals  :  — 

Electro-chemical  Equivalent  per 

equivalent  per  coulomb.  ampere-hour. 

Hydrogen     .     .     .     .000010354  grams  .03727    grams. 

Silver 00111800        "  4.0248 

Copper 0003284          "  1.1822 

Zinc 00033696        "  1.223056       " 

Lead 00107160        "  3.85776 

1  The  student  in  chemistry  will  understand  that  the  electro-chemical  equivalents 
of  different  metallic  elements  are  proportional  to  their  combining  equivalents. 


GALVANOMETER.  495 

Edison  in  his  system  of  electric  lighting  employs  a  zinc 
voltameter  for  measuring  the  quantity  of  electricity  furnished 
to  each  customer.  It  consists  of  two  zinc  plates  immersed  in 
a  solution  of  zinc  sulphate,  and  is  so  arranged  by  means  of  a 
divided  circuit  (§  477)  that  only  a  portion  (say  a  thousandth) 
of  the  current  passes  through  the  liquid.  The  increase  of 
mass  of  the  electro-negative  plate  in  grams  divided  by  1.223 
gives  the  quantity  in  ampere-hours  which  has  passed  through 
the  voltameter. 

In  like  manner  the  electrolytical  action  in  the  voltaic  cell 
itself  is  proportional  to  the  strength  of  the  current  while  it 
passes.  One  coulomb  of  electricity  in  passing  through  a 
Daniell's  cell  dissolves  .00033696  gram  of  zinc  and  deposits 
.0003284  gram  of  copper. 

A  coulomb-meter  will  serve  as  an  ampere-meter  (abbreviated, 
ammeter)  when  the  current  is  very  nearly  constant,  but  not 
otherwise.  For  the  quantity  of  electricity  measured  in 
coulombs  which  has  passed  through  the  circuit  in  a  given 
time,  divided  by  the  number  of  seconds,  obviously  gives  the 
coulombs-per-second,  or  the  mean  ampere  strength  of  the 
current. 

"465.  Galvanometer.  —  This  is  an  instrument  for  measuring 
current-strength  by  means  of  the  deflection  of  a  magnetic 
needle  when  placed  in  the  field  of  the  current.  It  is  so  con- 
structed that  either  the  deflection  angle  itself,  or  some 
function  of  it,  is  proportional  to  the  current-strength. 

466.  Thomson's  mirror  galvanometer. — A  simplified  form 
is  shown  in  Fig.  385,  and  the  complete  instrument  is  shown 
in  Fig.  386.  Insulated  wire  is  wound  on  a  bobbin,  A.  With- 
in this  bobbin  is  hung,  by  a  silk  fiber,  a  little  circular  concave 
mirror,  to  the  back  of  which  are  attached  little  magnets  of 
watch-spring  steel.  To  adjust  it  for  use,  the  suspended 
magnets  must  be  set  parallel  to  the  coil  of  wire.  For  this 
purpose  it  is  necessary  to  have  a  small  controlling  magnet, 


496 


ETHER    DYNAMICS. 


n  s,  to  cause  the  needles  to  take  the  required  position.  The 
galvanometer  is  also  rendered  more  or  less  sensitive  by  moving 
the  controlling  magnet  farther  from  or  nearer  to  the  needles. 


FIG.  385. 


If  a  beam  of  light  from  a  lamp  in  a  dark  room  be  thrown 
upon  the  mirror  and  reflected  thence  to  a  screen,  S,  a  spot  of 


FIG 


light  thereon  will  show  the  slightest  change  in  the  position 
of  the  mirror-needle  in  the  coil.     Hence  a  very  feeble  current 


TANGENT    GALVANOMETER. 


497 


declares  its  presence  by  causing  the  spot  of  light  to  move  to 
one  side  or  the  other  of  a  central  or  zero  point  where  the  spot 
falls  when  there  is  no  current.  With  this  galvanometer  no 
appreciable  error  is  committed  in  considering  the  current 
strengths  as  proportional  to  the  scale-readings.  This  instru- 
ment is  of  great  value  to  the  electrician  in  dealing  with  very 
weak  currents. 

467.  Tangent  galvanometer.  —  A  tangent  galvanometer  is 
one  so  constructed  that  the  current  passing  through  it  is  pro- 
portional to  the  tangent  of  the  angle  of  deflection  produced. 
To  this  end  it  is  necessary  that  the  needle  be  very  short  (not 
more  than  3^)  in  comparison  with  the  diameter  of  the  coil. 

In  its  simplest  form  it  consists  of  a  large  vertical  coil 
(better  two  coils,  one  on  each  side  of  the  needle,  Fig.  387, 
so  placed  that  the  needle  is 
at  the  center  of  the  common 
axis),  in  the  center  of  which 
is  either  a  small  compass 
needle  or  a  needle  suspended 
by  a  silk  fiber. 

A  needle  thus  placed  in  the 
field  of  a  current  is  acted  on 
by  a  mechanical  couple  tend- 
ing to  place  it  at  right  angles 
to  the  plane  of  the  coil,  and  it 
is  deflected  until  this  couple  is 
balanced  by  the  return  couple 
due  to  the  earth's  magnetism. 
The  value  of  the  earth's  mag- 
netic intensity  in  a  horizontal  plane  is  denoted  by  H. 

The  formula  for  the  tangent  galvanometer  is  C  =  — — -  tan  6  = 

2irn 

K  tan  6,  in  which  C  is  the  current  strength  in  C.G.S.  units  ;  H,  as 
above,  measured  in  dynes ;  6,  the  angle  of  deflection  ;  and  r,  the 


FIG.  387. 


498  ETHER    DYNAMICS. 

mean  radius  of  the  coil  of  n  turns.     K,  which  is  called  the  reduction 
factor  of  the  galvanometer,  is  usually  written  in  the  form 

K_    H    _H 

~      ' 


It  is  made  up  of  two  parts,  viz.  H,  which  is  dependent  on  locality, 
and  G,  which  depends  on  the  construction  of  the  instrument,  and  is 
therefore  called  the  galvanometer  constant.  Hence,  if  the  value  of 
H  and  G  be  once  found,  the  strength  of  any  current  is  calculated 
by  multiplying  the  tangent  of  the  deflection  angle  by  the  ratio  K. 
As  an  ampere  =  10—1  C.G.S.  unit,  the  current  strength  in  amperes 
is  found  by  multiplying  this  value  by  10. 

When  the  scale  is  divided  into  degrees,  the  corresponding  tan- 
gents are  found  by  consulting  a  table  of  tangents  (p.  626).  In  some 
instruments,  however,  the  scale  is  graduated  directly  in  tangents. 

The  process  of  finding  the  value  of  the  reduction  factor  of  any 
instrument  is  called  standardizing.  There  are  many  ways  of  doing 
this,  which  may  be  found  in  any  good  laboratory  manual.  One  of 
these  consists  in  introducing  a  copper  voltameter  into  circuit  with 
the  galvanometer.  After  passing  a  current  for  a  certain  time,  and 
observing  the  deflection  of  the  galvanometer  during  that  time,  ascer- 
tain the  gain  of  mass  in  grams  of  the  negative  plate,  and  divide  this 
gain  by  the  time  in  seconds.  This  gives  the  deposit  of  copper  per 
second.  Dividing  this  result  by  .0003284  (§  464)  gives  the  ampere 
current  which  passed  through  the  galvanometer.  Finally,  divide 
the  last  result  by  10  tan  6  and  the  result  is  the  value  of  K.  That 
is,  the  reduction  factor  of  a  galvanometer  =  strength  of  current  in 
amperes  -r  10  tan  0,  when  6  is  the  average  deflection.1 

It  has  been  found  that  errors  of  observation  affect  the  value  of  C 
least  when  the  mean  deflection  is  45°;  hence,  it  is  customary  to 
arrange  the  experiments  so  that  about  this  deflection  angle  may 
be  produced. 

If  the  strengths  of  two  currents  are  to  be  compared,  it  is 
only  necessary  to  obtain  deflections  with  each  current  sepa- 
rately, and  compare  the  tangents  of  the  angles. 

468.    Ammeter.  —  Now  if  the  value  of  each  division  of  the 

1  It  is  to  be  borne  in  mind  that  the  formula  C  =  K  tan  9  measures  the  current  in 
C.G.S.  electro-magnetic  units  and  not  in  amperes  ;  and  that  1  C.G.S.  unit  is  equal  to 
10  amperes. 


AMMETER. 


499 


scale  be  found  by  multiplying  the  number  indicating  the 
tangent  of  the  angle  of  deflection  by  10  K,  and  these  results 
be  placed  upon  the  scale  in  place  of  degree  numbers,  we  shall 
have  a  direct-reading  ampere-meter  (ammeter).  There  is  a 
great  variety  of  ammeters  in  use,  for  a  description  of  which 
the  student  is  referred  either  to  technical  works  on  the  sub- 
ject or  to  the  inventors  themselves. 

We  shall  consider  only  one  other  form,  that  called  the 
(Kohlrausch)  solenoid  ammeter,  selecting  this  because  of  its 
simplicity.  In  Fig.  388,  a  is  a  helix  of  thick  wire,  b  is  a  soft 
iron  tube  which  serves  as  a  core,  suspended  by  a  light  spring 


FIG.  388. 

c.  The  core  carries  a  marker  j ;  f  is  merely  a  wooden  guide- 
rod  for  the  tubular  core.  The  action  of  this  ammeter  depends 
upon  the  principle  that  when  an  insulated  wire  is  wound  into 
a  helix  (called  also  a  solenoid),  and  a  current  is  passed 
through  the  wire,  an  iron  rod  or  tube  placed  at  the  opening 
will  be  drawn  into  the  helix  with  a  force  increasing  with  the 


500  ETHER    DYNAMICS. 

strength  of  the  current.  This  force  acting  against  the  elastic 
force  of  the  spring  may  be  measured  in  the  same  manner  as 
weight  by  a  spring  balance.  Now  as  the  current  strength 
bears  a  definite  relation  to  the  force,  the  instrument  can 
easily  be  calibrated  in  amperes. 

SECTION  IX. 

RESISTANCE  OF  CONDUCTORS. 

469.  External  and  internal  resistance.  —  For  convenience 
the  resistance  of  an  electric  circuit  is  divided  into  two  parts, 
the  external  and  the  internal.     External  resistance  includes 
all  the  resistance  of  a  circuit  except  that  of  the  generator, 
while  the  latter  is  termed  internal  resistance. 

When  the  external  resistance  in  a  circuit  is  considered 
separately  from  the  internal,  Ohm's  formula  must  be  con- 
verted thus  (calling  the  former  R,  and  the  latter  r) :  — 

C__E_ 
-R  +  r 

If  a  cell  have  E  =  l  volt,  and  r=l  ohm,  and  the  connecting 
wire  be  short  and  stout,  so  that  R  may  be  disregarded,  then 
the  cell  yields  a  current  of  one  ampere.  If  by  any  means 
the  internal  resistance  of  this  cell  can  be  decreased  one-half, 
it  will  then  be  capable  of  yielding  a  two-ampere  current 
under  the  same  conditions. 

470.  External  resistance. 

Experiment!. — Introduce  into  a  circuit  a  galvanometer,1  and  note 
the  number  of  degrees  the  needle  is  deflected.  Then  introduce  into  the 

1  The  galvanometer  represented  in  the  cut  is  a  form  of  galvanometer  chiefly  used 
by  the  author  in  elementary  laboratory  work.  The  results  obtained  by  it  are  ap- 
proximately those  which  would  be  obtained  by  a  standard  tangent  galvanometer. 
The  manifold  uses  to  which  galvanometers  are  put  in  a  physical  laboratory  properly 
require  a  variety  of  instruments,  and  this  would  make  a  complete  equipment  quite 
expensive. 


EXTERNAL    RESISTANCE. 


501 


same  circuit  the  wire  on  the  spool  numbered  4  on  the  platform,2  S 
(Fig.  389).  (The  wire  on  any  one  of  the  five  spools  on  this  platform  can 
at  any  time  be  introduced  into  a  circuit,  by  connecting  the  battery  wires 
with  the  binding  screws  on  each  side  of  the  spool  to  be  introduced.) 


FIG.  389. 


The  deflection  is  now  less  than  before.  The  copper  wire  on  this  spool 
is  16  yards  in  length ;  its  size  is  No.  30  of  the  Brown,  and  Sharpe  wire 
gauge.  When  this  spool  is  in  circuit,  the  circuit  is  16  yards  longer  than 
when  the  spool  is  out.  The  effect  of  lengthening  the  circuit  is  to  weaken 
the  current,  as  shown  by  the  diminished  deflection. 

Experiment  2.  —  Next,  substitute  Spool  2  for  Spool  4.  This  contains 
32  yards  of  the  same  kind  of  wire  as  that  on  Spool  4.  The  deflection  is 
still  smaller. 

The  weakening  of  the  current  by  introducing  these  wires  is  caused  by 
the  resistance  which  the  wires  offer  to  the  current,  much  as  the  friction 
between  water  and  the  interior  of  a  pipe  impedes,  to  some  extent,  the 
flow  of  water  through  it.  The  longer  the  pipe  the  greater  is  the  re- 
sistance to  the  flow. 

If  the  wire  on  the  spools  had  been  the  only  resistance  in  the  circuit, 
then,  when  Spool  2  was  in  the  circuit,  the  resistance  would  have  been 
double  what  it  was  when  Spool  4  was  in  the  circuit,  and  the  current, 
with  double  the  resistance,  would  have  been  half  as  strong. 

2  The  platform  of  spools  containing  wire  of  different  (known)  sizes,  lengths,  and 
material,  so  arranged  that  any  one,  two,  or  more  can  be  introduced  into  the  circuit 
for  the  purpose  of  measurement  of  resistance,  is  an  instrument  of  great  convenience 
in  a  school  laboratory. 


502  ETHER   DYNAMICS. 

(1)  Other  things  being  equal,  the  resistance  of  a  conductor 
varies  as  its  length. 

Experiment  3.  —  Next  substitute  Spool  1  for  Spool  2.  This  spool 
contains  32  yards  of  No.  23  copper  wire,  —  a  thicker  wire  than  that  on 
Spool  2,  but  the  length  of  the  wire  is  the  same.  The  deflection  is  now 
greater  than  it  was  when  Spool  2  was  in  circuit.  This  indicates  that  the 
larger  wire  offers  less  resistance. 

Careful  experiments  show  that  (2)  the  resistance  of  all 
conductors  varies  inversely  as  the  areas  of  their  cross  sections. 
If  the  conductors  be  cylindrical  it  varies  inversely  as  the  square 
of  their  diameters. 

Experiment  4. — Substitute  Spool  5  for  Spool  1,  and  compare  the 
deflection  with  that  obtained  when  Spool  4  was  in  the  circuit.  The  de- 
flection is  smaller  than  when  Spool  4  was  in  circuit.  The  wire  on  these 
two  spools  is  of  the  same  length  and  size,  but  the  wire  of  Spool  5  is  Ger- 
man-silver. It  thus  appears  that  German-silver  offers  more  resistance 
than  copper. 

(3)  In  obtaining  the  resistance  of  a  conductor,  the  specific 
resistance  of  the  substance  must  enter  into  the  calculation. 
(See  table  of  specific  resistances  in  the  Appendix.) 

The  resistance  of  metal  conductors  increases  slowly  with 
the  temperature  of  the  conductor.  The  resistance  of  German- 
silver  is  affected  less  by  changes  of  temperature  than  that  of 
most  metals ;  hence  its  general  use  in  standards  of  resistance. 

471.    Internal  resistance. 

Experiment  5.  —  Connect  with  the  galvanometer  the  copper  and  zinc 
strips  used  in  Experiment  1,  Section  1,  and  introduce  the  strips  into  a 
tumbler  nearly  full  of  acidulated  water.  Note  the  deflection.  Then  raise 
the  strips,  keeping  them  the  same  distance  apart,  so  that  less  and  less  of 
the  strips  will  be  submerged.  As  the  strips  are  raised,  the  deflection  be- 
comes smaller.  This  is  caused  by  the  increase  of  resistance  in  the  liquid 
part  of  the  circuit,  as  the  cross  section  of  the  liquid  lying  between  the 
two  strips  becomes  smaller. 


DESCRIPTION    OF    THE    RESISTANCE    BOX. 


503 


(4)  The  internal  resistance  of  a  circuit,  other  things  being 
equal,  varies  inversely  as  the  area  of  the  cross  section  of  the 
liquid  between  the  two  elements. 

In  a  large  cell  the  area  of  the  cross  section  of  the  liquid 
between  the  elements  is  larger  than  in  a  small  cell,  con- 
sequently the  internal  resistance  is  less.  This  is  the  only 
way  in  which  the  size  of  the  cell  affects  the  current. 

Obviously  the  resistance  of  the  battery  would  be  increased 
by  any  increase  of  the  distance  between  the  elements,  since 
this  increases  the  length  of  the  liquid  conductor,  but  as  this 
distance  is  usually  made  as  small  as  convenient,  and  is  kept 
invariable,  it  demands  little  of  our  attention. 


SECTION   X. 

MEASUREMENT    OF    RESISTANCE. 

472.    Description  of  the  resistance  box. 

Fig.  390  represents  a  wooden  box  containing  what  is  equivalent  to  a 
series  of  coils  of  German-silver  wire,  whose  resistance  ranges  from  0. 1  ohm 
to  100  ohms.1  Each  of 
these  coils  is  connected 
with  a  brass  stud  on  the 
top  of  the  box. 

Three  switches,  A, 
B,  and  C,  so  connect 
the  coils  with  the  bind- 
ing screws  a  and  6  that 
a  current  can  be  sent 
through  any  three  coils 
at  the  same  time  by 

moving  the  switches  on  FlG  390 

to    the    proper    studs. 

The  resistance  in  ohms  of  each  coil  is  marked  on  the  box  near  its  stud. 
When  the  three  switches  rest  upon  studs  marked  0,  the  current  meets 
with  no  appreciable  resistance  in  passing  through  the  box,  but  any 


1  Each  additional  switch  with  its  corresponding  coils,  increases  the  range  about 
tenfold,  so  that  the  range  of  the  instrument  may  be  very  much  increased. 


504 


ETHER    DYNAMICS. 


G     G     X 


PIG.  391. 


desired  resistance  within  the  range  of  the  instrument  can  be  introduced 
by  moving  the  switches  on  to  the  studs,  the  sum  of  whose  resistances  is 
the  resistance  required.  This  instrument  we  shall  call  a  resistance  box. 

473.     Wheatstone  bridge. 

Fig.  391  represents  a  perspective  view  of  the  bridge  (as  modified 
by  the  author),  and  Fig.  392  represents  a  diagram  of  the  essential 
electrical  connections.1     The  battery  wires  are  connected  with  the 
bridge  at  the  binding  screws  B  B'.     A  galvanometer,  (?,  is  con- 
nected at  GG',  a  resist- 
R  "?  ance  box,  r,  at  R  R,  and 

the  conductor  x,  whose 
resistance  is  sought,  at 
XX. 

When  the  circuit  is 
closed  by  means  of  the 
key  T,  the  current,  we 
will  suppose,  enters  at  B  ; 

on  reaching  the  point  A  it  divides,  one  part  flowing  ma  the  branch 
A  G  B',  and  the  other  ma,  the  branch  A  D  B'.  If  points  D  and  G 
in  the  two  branches  be  at 
different  potentials  and  a 
connection  be  made  be- 
tween them  through  the 
galvanometer,  G,  by  clos- 
ing the  key  S,  there  will 
be  a  current  through  this 
wire  and  through  the  gal- 
vanometer, and  a  deflec- 
tion of  the  needle  will  be 
produced.  But  if  the 
points  D  and  G  be  at 
the  same  potential,  there 
will  be  no  cross  current 
through  the  bridge  wire 
and  no  deflection.  Now 
it  can  be  demonstrated 
that  points  D  and  G  will  be  at  the  same  potential  when  R  (the  re- 

1  The  student  will  find  descriptions  of  the  more  elaborate  bridges  and  resistance 
coils  in  such  works  as  Gordon's  Electricity  and  Magnetism,  Vol.  I,  Sylvanus  Thomp- 
son's Lessons  in  Electricity  and  Magnetism,  and  in  various  laboratory  manuals. 


B    I 


WHEATSTONE    BRIDGE.  505 

sistance)  of  A 1)  :  R  of  D  B' : :  R  of  A  G  :  R  (the  unknown  resistance) 
of  G  B'.  Between  A  and  D  and  A  and  G  there  are  three  coils  of 
wire  having  resistances  respectively  of  1,  10,  and  100  ohms.  One  or 
more  of  these  coils  are  introduced  into  the  circuit  by  removing  the 
corresponding  plugs  a,  5,  c,  d,  e,  and  /.  As  the  other  connections 
between  A  and  D,  and  A  and  G,  have  no  appreciable  resistance, 
being  for  the  most  part  short  brass  bars,  the  only  practical  resist- 
ance between  these  points  is  that  introduced  at  will  through  the 
coils.  Similarly  between  points  D  and  B',  the  only  practical  resist- 
ance is  that  introduced  at  will  through  the  resistance  box,  and 
between  the  points  G  and  B'  the  resistance  is  the  resistance  (x) 
sought. 

It  is  apparent,  then,  that  in  using  the  bridge  after  the  connec- 
tions are  properly  made  through  the  several  instruments  and  certain 
known  resistances  are  introduced  between  A  and  D,  and  A  and  G, 
we  have  simply  to  regulate  the  resistance  through  the  resistance 
box  so  that  there  will  be  no  deflection  in  the  galvanometer ;  then 
we  are  sure  that  the  above  proportion  is  true.  The  first  three 
terms  of  the  proportion  being  known,  the  fourth  term,  which  is  the 
resistance  sought,  is  computable.1 

If  the  same  resistance  be  introduced  between  points  A  and 
(r  as  between  A  and  D?  it  is  evident  that  the  resistance  in 
the  resistance  box  r  must  be  made  equal  to  the  unknown 
resistance  x  in  order  that  there  may  be  no  deflection  in  the 
galvanometer.  Consequently  when  this  result  is  obtained 
the  resistance  of  x  may  be  read  from  the  resistance  box. 

Experiment.  —  Measure  the  resistance  of  each  of  the  several  spools  of 
wire  used  above, — electro-magnets,  electric  lamps,  etc.,  —  using  the 
bridge.  Place  the  switches  of  the  resistance  box  on  the  zero  studs. 
Make  connections  as  in  the  description  above.  Then  close  the  circuit  at 

1  The  accuracy  of  the  results  obtained  largely  depends  upon  so  choosing  resist- 
ances of  the  bridge  as  to  make  the  arrangement  have  maximum  sensibility,  and  upon 
the  sensitiveness  of  the  galvanometer.  In  using  the  bridge  the  following  directions 
should  be  observed  :  (1)  Always  close  the  circuit  at  T  before  closing  the  bridge  at  S, 
and  in  breaking  the  circuit  reverse  this  order.  (2)  Introduce  between  A  and  D,  and 
A  and  G,  resistance  as  nearly  equal  to  the  resistance  sought  (x)  as  practicable.  If 
you  have  no  conception  what  the  unknown  resistance  is,  it  is  best  to  begin  by  using 
high  resistances.  (3)  Use  a  sensitive  galvanometer,  e.g.  a  mirror  galvanometer,  or 
the  galvanometer  shown  in  Fig.  389,  substituting  the  astatic  needle  for  the  tangent 
needle. 


506 


ETHER   DYNAMICS. 


B' 


T,  and  afterwards  the  bridge  at  S.  There  will  probably  be  a  deflection 
in  the  galvanometer.  Regulate  the  resistance  through  the  resistance 
box,  throwing  in  or  taking  out  resistance  according  as  one  or  the  other 
tends  to  reduce  the  deflection  (the  process  is  much  like  that  of  weighing), 
until  there  is  no  deflection.  Then  compute  the  resistance  sought  accord- 
ing to  the  above  proportion. 

474.  Measurement  of  galvanometer  resistance.    Lord  Kelvin' 's 
method.  —  The  bridge  may  be  used  for  measuring  the  resist- 
ance of  the  galvanometer  actually  in 
use.     The  bridge  is  arranged  as  in 
Fig.  393.     The  resistance  in  the  re- 
sistance box  R  is  then  varied  until 
the  deflection  of  G  does  not  change 
when  the  key  S  is  closed  ;  then 

a 

r  =  l&-> 
b 

in  which  r  is  the  resistance  of  the 
galvanometer,  R  is  the  resistance  in 
the  resistance  box,  and  a  and  b  are  the 
resistances  in  the  arms  A  G'  and  A  D 
respectively.  If  a  =  b,  then  r  =  R. 

475.  Battery  resistance.     Mance's  method. 

No  definite  meaning  can  be  attached  to  the  expression  battery 
resistance,  since  this  resistance  is  complicated  by  variation  in  the 
polarization,  and  this  in  turn  is  dependent  upon  the  strength  of  the 
current,  external  resistance,  etc.  Hence  the  numerous  methods 
depending  on  Ohm's  law  that  have  been  devised  for  deducing  battery 
resistance  are  of  little  value  in  many  cases. 

The  method  known  as  Mance's  method  is  one  of  the  best  for 
measuring  battery  resistance,  since  it  requires  the  battery  to  be 
constant  only  during  the  short  time  the  key  is  closed.  A  Wheat- 
stone  bridge  is  arranged  as  shown  in  Fig.  394.  The  resistance  in 
the  resistance  box  R  is  adjusted  until,  on  pressing  down  the  key 
A,  the  deflection  of  the  galvanometer  does  not  change ;  then 


ELECTRO-MOTIVE    FORCE    OF    DIFFERENT    CELLS.    507 

in  which  r  is  the  battery  resistance,  R  is  the  resistance  in  the  re- 
sistance box ;  a  and  b  are  the  resistances  respectively  in  the  arms 
A  G'  and  AD.     If  a  =  6,  the  for- 
mula is  simplified,  and  becomes 
r-R. 

The  information  generally  re- 
quired in  practice,  however,  is 
what  available  difference  of  po- 
tentials can  be  obtained  with  a 
certain  working  resistance  in  the 
external  circuit.  This  can  be 
obtained  by  connecting  the  ter- 
minals of  the  battery  by  the 
body  offering  this  resistance,  and 
measuring  the  difference  of  po- 
tentials between  these  points  by 
means  of  a  potential  galvanom- 
eter. If  we  call  this  difference  FlG  394 
of  potentials  V,  and  the  E.M.F. 

of  the  battery  when  on  open  circuit  E,  and  R  =  external  resistance, 
then  we  may  write 

E    -v-r 

R+r~R- 

where  r  is  such  a  quantity  as  satisfies  this  equation.  In  other 
words,  this  quantity  may  be  taken  as  the  resistance  of  the  battery 
for  the  current  C. 


SECTION   XI. 


E.M.F.    OF    DIFFERENT    CELLS.         DIVIDED    CIRCUITS. 
OF    COMBINING    VOLTAIC    CELLS. 


METHODS 


476.  Electro-motive  force  of  different  cells.  —  If  a  galva- 
nometer be  introduced  into  a  circuit  with  different  battery  cells, 
e.g.  Bunsen,  Daniell,  Grenet,  etc.,  very  different  deflections 
will  be  obtained,  showing  that  the  different  cells  yield  cur- 
rents of  different  strengths.  This  may  be  in  some  measure 
due  to  a  difference  in  their  internal  resistance,  but  it  is  chiefly 
due  to  the  difference  in  their  electro-motive  forces.  We 


508  ETHEK    DYNAMICS. 

learned  (§  431)  that  difference  of  electro-motive  force  is 
due  to  the  difference  of  the  chemical  action  on  the  two  plates 
used,  and  this  depends  upon  the  nature  of  the  substances 
used.  It  is  wholly  independent  of  the  size  of  the  plates  ; 
hence  the  electro-motive  force  of  a  large  battery  cell  is  no 
greater  than  that  of  a  small  one  of  the  same  kind.  Conse- 
quently any  difference  in  strength  of  current  yielded  by 
battery  cells  of  the  same  kind,  but  of  different  sizes,  is  due 
wholly  to  a  difference  in  their  internal  resistances. 

The  electro-motive  forces  of  the  Bunsen,  Daniell,  and 
Grenet  cells  are  respectively  about  1.8,  1,  and  2  volts. 

477.    Divided  circuits ;   shunts. 

Experiment  1.  —  Make  a  divided  circuit  as  in  Fig.  395  (using  double 
connectors  a  and  6).  Insert  a  galvanometer,  G,  in  one  branch  and  a 
resistance  box,  R,  in  the  other.  When  the  current 
reaches  a,  it  divides,  a  portion  traversing  one  branch 
through  the  galvanometer,  and  the  remainder  passing 
through  the  other  branch  and  the  resistance  box.  The 
branch  a  R  6  is  called  a  shunt  or  derived  circuit.  In- 
crease gradually  the  resistance  in  the  resistance  box. 
The  result  is  that  it  throws  more  of  the  current 
through  the  galvanometer,  as  shown  by  the  increase  of 
FIG.  395.  deflection. 

In  a  divided  circuit  the  current  divides  between  the  paths 
inversely  as  their  resistances.  For  example,  if  the  resistance 
of  the  resistance  box  above  be  4  ohms,  and  the  resistance  in 
the  galvanometer  be  1  ohm,  then  four-fifths  of  the  current  will 
traverse  the  latter  and  one-fifth  the  former. 

Suppose  that  the  resistance  box  and  galvanometer  be 
removed  from  the  shunts,  and  that  the  shunts  be  of  the 
same  length,  size,  and  kind  of  wire,  and  consequently  have 
equal  resistances.  Using  the  two  wires  instead  of  one  to 
connect  a  and  b  is  equivalent  to  doubling  the  size  of  this 
portion  of  the  conductor  ;  consequently  the  resistance  of  this 
portion  is  reduced  one-half. 


KIRCHHOFF  S    LAW. 


509 


Generally,  the  joint  resistance  of  two  branches  of  a  circuit  is 
the  product  of  their  respective  resistances  divided  by  their  sum. 
478.    Kirchhoff's  law. 


First 


The  following  discussion  will  make  the  above  law  evident, 
it  should  be  understood  that  when 
a  conductor  conveys  a  constant 
current  the  strength  of  current 
across  all  cross  -  sections  of  the 
conductor,  as  A,  C,  E  F,  D,  and 
B  (Fig.  396),  is  the  same.  Hence 
the  current  arriving  at  C  or  D  of 
the  main  circuit  is  equal  to  the 
sum  of  the  currents  which  flow 
by  the  branches  ri,  r%  and  r^. 
This  is  known  as  Kirchhoff's  First 
Law. 

By  Ohm's  law  if  two  points,  a 
and  6,  between  which  a  differ- 
ence of  potential  V  is  maintained, 
be  connected  by  two  wires  having  resistances  r\  and  r%,  the 

V  V 

current  in  that  of  resistance  r  i  will  be  — '    and  in  the  other  —  • 

If  C  be  the  whole  current  flowing  in  the  circuit,   we  have  by 
Kirchhoff's  law 


where  R  is  the  resistance  of  a  wire  which  might  be  substituted  for 
the  divided  conductor  between  a  and  6  without  affecting  the  cur- 
rent. Hence 

1.11  r\  r-2 

-  H =  —  '  and  R  =  —        —  • 

PI      J*2        R  r\  +  rg 

If  there  be  three  separate  wires  of  resistance,  as  in  Fig.  396,  we 
shall  have  in  a  similar  manner 


rs 


The  reciprocal  of  the  resistance  R  of  a  wire,  i.e.  ^ »  is  called  its 

R 

conductivity,  sometimes  expressed  as  mhos.1     We  may  say,  there- 
1  A  word  formed  by  writing  the  word  ohm  in  reverse  order. 


510  ETHER    DYNAMICS. 

fore,  in  general,  when  two  points  in  a  circuit  are  connected  by  a 
multiple  arc  (a  term  in  common  use  to  denote  a  divided  circuit 
between  any  two  points)  consisting  of  n  branches,  the  conductivity 
of  the  multiple  arc  is  equal  to  the  sum  of  the  conductivities  of  the  n 
branches :  in  other  words,  the  reciprocal  of  its  resistance  is  equal  to 
the  sum  of  the  reciprocals  of  the  resistances  of  its  branches. 

479.  Shunted  galvanometer.  —  When  a  current  is  so  strong 
as  to  produce  too  violent  an  impulse  upon  the  needle  of  a 
galvanometer,  its  terminals  may  be  shunted  through   a   re- 
sistance box,  so  that  any  known  fraction  of  the  current  may 
be  deflected  through  the  shunt.     For  example,  if  the  shunt 
have  a  resistance  ^  as  great  as  that  of  the  galvanometer,  then 
the -current  through  the  latter  will  be  ^  that  through   the 
shunt,  or  T^  of  the  total  current. 

480.  Methods  of  combining  cells. 

Experiment  2.  —  Take  two  Bunsen  cells,  and  connect  the  two  zinc 
plates  by  a  wire.  Then  connect  each  of  the  carbon  plates  with  a  gal- 
vanometer. The  E.M.F.  of  each  cell  would  tend  to  send  a  current 
opposite  to  that  of  the  other  cell.  But  you  find  that  there  is  either  no 
deflection  in  the  galvanometer,  or  at  most  a  very  small  one,  and  this 
shows  either  that  there  is  no  current  or  that  the  current  is  very  weak. 
The  reason  is  evident.  You  have  connected  two  carbons,  which  have 
the  same  potential,  through  the  galvanometer  ;  consequently  there  should 
be  no  current  between  them.  The  cells  are  said  to  be  connected  in 
opposition. 

A  very  simple  way  of  showing  that  a  large  cell  has  no 
greater  electro-motive  force  than  a  small  one  is  to  connect 
two  such  cells  in  opposition  through  a  galvanometer,  or, 
what  answers  the  same  purpose,  raise  the  zinc  of  one  of  two 
cells  of  the  same  size,  connected  in  opposition,  nearly  out  of 
the  liquid.  The  absence  of  a  current  shows  that  the  two 
carbons  have  the  same  potential,  and  consequently  their 
electro-motive  force  is  the  same. 

A  number  of  cells  connected  in  such  a  manner  that  the 
currents  generated  by  all  have  the  same  direction  constitutes 
a  voltaic  battery. 


BATTERIES   OF   LOW   INTERNAL   RESISTANCE.       511 


The  object  of  combining  cells  is  to  get  a  stronger  current 
than  one  cell  will  afford.     We  learn  from  Ohm's  law  that 
there  are  two,  and  only  two,  ways  of  increasing  the  strength 
of  a  current.     It  must  be  done  either  by  increasing 
the  E.M.F.  or  by  decreasing  the  resistance.     So 
we  combine  cells  into  batteries,  either  to  secure 
greater  E.M.F.  or  to  diminish  the  internal  resist- 
ance.     Unfortunately,   both  purposes    cannot   be 
accomplished  by  the  same  method. 

481.  Batteries  of  low  internal  resistance. — Fig. 
397  represents  three  cells  having  all  the  carbon  (+) 
plates  electrically  connected  with  one  another,  and 
all  the  zinc  (— )  plates  connected  with  one  another, 
and  the  triplet  carbons  are  connected  with  the 
triplet  zincs  by  the  •  leading-out  wires  through  a 
galvanometer  G-. 

It  is  easy  to  see  that  through  the  battery  the 
circuit  is  divided  into  three  parts,  and  consequent- 
ly the  conductivity  in  this  part  of  the  circuit,  ac- 
cording to  the  principle  stated  in  §  478,  must  be 
increased  threefold  ;  in  other  words,  the  internal 
resistance  of  the  three  cells  is  one-third  of  that  of  a  single 
cell.  This  is  called  connecting  cells  "  in  multiple  arc,"  and 
the  battery  is  called  a  "  battery  of  low  internal  resistance." 
The  resistance  of  the  battery  is  decreased  as  many  times  as 
there  are  cells  connected  in  multiple  arc,  but  the  E.M.F.  is 
that  of  one  cell  only. 

The  formula  for  the  current  strength  in  this  case  is  written 

thus :  E 

P -^ 

\j  —  •> 


FIG.  397. 


in  which  n  represents  the  number  of  cells.      It  is  evident 

IT 

from  this  formula  that  when  K  is  so  great  that  -  is  a  small 

n 


512  ETHER    DYNAMICS. 

part  of  the  whole  resistance  of  the  circuit,  little  is  added  to 
the  value  of  C  by  increasing  the  number  of  cells  in  multiple 
arc. 

482.    Batteries  of  high  internal  resistance  and  great  E.M.F. 

—  Fig.  398  represents  four  cells  having  the  carbon  or  +  plate 

of  one  connected  with  the  zinc  or  —  plate  of  the  next,  and 

the  +  plate  at  one  end  of  the 
series  connected  by  leading-out 
wires  through  a  galvanometer 
with  the  —plate  at  the  other 
end  of  the  series.  It  is  evi- 
dent  that  the  current  in  this 
series  traverses  the  liquid  four 
times,  which  is  equivalent  to 

lengthening  the  liquid  conductor  four  -times,  and  of  course 
increasing  the  internal  resistance  fourfold.  But,  while  the 
internal  resistance  is  increased,  the  E.M.F.  of  the  battery  is 
increased  as  many  times  as  there  are  cells  in  series.  The  gain 
by  increasing  the  E.M.F.  more  than  offsets,  in  many  cases 
(always  when  the  internal  resistance  is  a  small  part  of  the 
whole  resistance  of  the  circuit),  the  loss  occasioned  by  in- 
creased resistance. 

The  formula  for  current  strength  in  this  case  becomes 

- 


It  is  evident  that  C  is  increased  most  by  adding  cells  in 
series  when  n  r  is  smallest  in  comparison  with  R. 

483.    Best  arrangement  of  cells. 

Experiment  3.  —  Introduce  into  circuit  with  a  single  cell  a  resistance 
box  and  a  galvanometer.  Throw  a  resistance  of  (say)  50  ohms  into  the 
circuit  by  means  of  the  resistance  box.  Note  the  deflection.  Then  add 
another  cell,  in  series,  to  the  cell  already  in  use.  The  deflection  is  con- 
siderably increased.  Other  cells  may  be  added  with  similar  results. 

Experiment  4>  ~  Connect  the  two  cells  in  multiple  arc,  keeping  the 


BEST    ARRANGEMENT    OF    CELLS.  513 

same  resistance  in  the  resistance  box.  The  deflection  is  only  a  very  little 
greater  than  that  caused  by  a  single  cell. 

Experiment  5.  —  Connect  a  single  cell  with  a  galvanometer  of  low 
resistance,  so  that  the  whole  external  resistance  may  be  less  than  the 
resistance  of  the  single  cell.  Note  the  deflection.  Then  introduce  an- 
other cell  in  multiple  arc.  The  deflection  is  considerably  increased. 

Experiment  6.  —  Connect  the  same  cells  in  series.  The  deflection 
differs  but  little  from  that  produced  by  a  single  cell. 

Hence,  (1)  ivfien  the  external  resistance  is  large,  connect  cells 
in  series ;  (2)  when  the  external  is  less  than  the  internal  re- 
sistance, connect  cells  in  multiple  arc. 

The  two  systems  may  be  combined  in  one  battery.  Thus 
one  pair  in  series  may  be  placed  in  multiple  arc  with  another 
pair  in  series.  This  combination  would  give  double  the 
E.M.F.  of  a  single  cell,  but  the  resistance  of  only  one  cell. 

With  a  given  number  of  cells  and  a  given  external  resistance 
the  maximum  current  is  generated  when  the  external  and  in- 
ternal resistances  are  equal.  It  is  seldom  possible  in  practice 
so  to  join  the  cells  as  to  fulfill  this  condition ;  but  if  the 
strongest  possible  current  be  required  it  should  be  fulfilled 
as  nearly  as  possible.  The  fallacy,  however,  of  introducing 
resistance  into  any  part  of  the  circuit  for  the  purpose  of 
making  these  resistances  equal  must  be  carefully  avoided, 
for  resistance  wherever  introduced  can  tend  only  to  weaken 
the  current.  Nor  must  it  be  supposed  that  of  two  batteries 
of  equal  E.M.F.,  but  one  having  a  high,  the  other  a  low  re- 
sistance, the  former  is  better  adapted  for  working  through  a 
high  resistance.  It  should  be  borne  in  mind  that  the  role  of 
a  battery  in  general  is  to  maintain  a  difference  of  potential 
between  its  poles,  and  the  element  of  resistance  that  it  intro- 
duces into  the  circuit  is  a  necessary  evil,  not  to  be  voluntarily 
increased. 

Electro-magnets  and  galvanometers  must  be  adapted  to  the 
circuits  in  which  they  are  to  be  placed.  In  connection  with 
the  above  discussion,  it  seems  proper  to  introduce,  somewhat 


514  ETHER    DYNAMICS. 

parenthetically,  a  few  facts  pertaining  to  the  use  of  electro- 
magnets and  galvanometers. 

In  order  to  produce  the  greatest  effect,  the  resistance  of  the 
helix  of  an  electro-magnet  should  be  equal  to  that  of  the  portion 
of  the  circuit  not  included  in  the  helix,  i.e.  to  the  rest  of  the 
circuit.  When  several  electro-magnets  are  used  in  the  same 
circuit,  the  sum  of  the  resistances  of  all  the  helices  should  be 
equal  to  the  resistance  of  the  rest  of  the  circuit. 

The  same  rule  applies  to  galvanometers.  High  resistance 
galvanometers  are  most  suitable  for  high  resistance  circuits, 
and  low  resistance  galvanometers  are  most  suitable  for  low 
resistance  circuits.  In  other  words,  both  galvanometers  and 
electro-magnets  should  be  adapted  to  the  resistance  of  the 
circuit  in  which  they  are  to  be  used. 

Exercises. 

1.  What  E.M.F.  is  required  to  maintain  a  current  of  one  ampere 
through  a  resistance  of  one  ohm  ? 

2.  Through  what  resistance  will  an  E.M.F.  of  ten  volts  maintain  a 
current  of  5  amperes  ? 

3.  What  current  ought  an  E.M.F.  of  20  volts  to  maintain  through  a 
resistance  of  5  ohms  ? 

4.  A  voltmeter  applied  each  side  of  an  electric  lamp  shows  a  differ- 
ence of  potential  of  40  volts ;  what  current  flows  through  the  lamp,  if  it 
have  a  resistance  of  10  ohms  ? 

5.  The  resistance  between  two  points  in  a  circuit  is  10  ohms.     An 
ammeter  shows  that  there  is  a  current  strength  in  the  circuit  of  0.5 
ampere  ;  what  is  the  difference  in  potential  between  the  points  ? 

6.  What  current  will  a  Bunsen  cell  furnish  when  r  =  0.9  ohm  (about 
the  resistance  of  a  quart  cell),  E  =  1.8  volts,  and  R  =  0.01  ohm  (about 
the  resistance  of  3  ft.  of  No.  16  wire)  ? 

[In  the  following  exercises,  whenever  a  Bunsen  cell  is  mentioned  it 
may  be  understood  to  be  a  quart  cell,  having  a  resistance  of  about  0.9 
ohm.  Its  E.M.F.  is  about  1.8  volts.] 

7.  a.  When  is  a  large  cell  considerably  better  than  a  small  one  ? 
6.  When  does  the  size  of  the  cell  make  little  difference  in  the  current '? 

8.  If  you  have  a  dozen  quart  cells,  how  can  you  make  them  equiva- 
lent to  one  3-gallon  cell  ? 


EXERCISES.  515 

9.  If  a  battery  of  10  cells  have  an  E.M.F.  ten  times  greater  than 
that  of  a  single  cell,  why  will  not  the  battery  yield  a  current  ten  times 
as  strong  ? 

10.  a.  The  internal  resistance  of  ten  cells,  connected  in  multiple  arc, 
is  what  part  of  that  of  a  single  cell  ?     b.  If  the  cells  were  connected  in 
series,  how  would  the  resistance  of  the  battery  compare  with  that  of  one 
of  its  cells?     c.  How  would  the  E.M.F.  of  the  latter  battery  compare 
with  that  of  a  single  cell  ? 

11.  What  current  will  a  single  Bunsen  cell  furnish  through  an  external 
resistance  of  10  ohms  ? 

12.  What  current  will  8  Bunsen  cells,  in  series,  furnish  through-  the 
same  resistance  ? 

SOLUTE  :        ^  =  10+8ftX98x8  =  0.83  +  ampere. 

13.  What  current  will  8  Bunsen  cells,  in  multiple  arc,  furnish  through 
the  same  external  resistance  ? 


=  0.  17  +  ampere. 


10  .K  8) 

14.  What  current  will  a  Bunsen  cell  furnish  through  an  external  re- 
sistance of  0.4  ohm  ? 

15.  What  current  will  a  battery  of  two  Bunsen  cells,  in  series,  furnish 
through  the  same  resistance  as  the  last  ? 

16.  What  current  will  two  cells,  in  multiple  arc,  furnish  through  the 
same  resistance  ? 

17.  A  coil  of  wire  having  a  resistance  of  10  ohms  carries  a  current  of 
1.5  amperes.     Required  the  difference  of  potential  at  its  ends. 

18.  What  would  be  the  resistance  at  0°  C.  of  a  column  of  mercury 
154  cm  long  and  f  of  a  square  millimeter  in  cross-section  ? 

19.  a.  What  is  the  resistance  of  £  mile  of  No.  16  (diam.  .05  in.)  copper 
wire?     6.  What  E.M.F.  will  be  required  to  maintain  a  current  of  .5 
ampere  in  this  circuit  ? 

20.  a.  The  resistance  between  two  points,  A  and  B,  of  a  conductor  is 
2.5  ohms  ;  the  resistance  of  a  shunt  between  the  same  points  is  1.5  ohms  ; 
what  is  the  joint  resistance  between  these  points  ?    b.  If  a  current  of  10 
amperes  be  maintained  between  these  points,  what  will  be  the  strength 
of  current   in   each  branch?     c.  How  would  the   strength   of  current 
between  these  points  be  affected  if  the  shunt  be  removed  and  the  same 
fall  of  potential  be  preserved  ?     Why  ? 

21.  a.  Points  A  and  B  in  a  circuit  are  connected  in  multiple  arc  by 
three  branches  whose  respective  resistances  are  2,  3,  and  4  ohms.     State 


516  ETHER    DYNAMICS. 

in  order  their  relative  conductivities,     b.  State  the  joint  conductivity  of 
the  multiple  arc.     c.  State  the  joint  resistance  of  the  multiple  arc: 

22.  Four  conductors  in  multiple  arc  have  resistances  of  100,  50,  27, 
and  19  ohms.     What  is  their  combined  resistance  ?    Ans.  8.3  ohms. 

23.  Assume  a  current  of  30  amperes  and  an  E.M.F.  of  50  volts ;  what 
is  the  resistance  and  conductivity  ? 

24.  A  wire  is  40  mils  (a  mil  is  .001  in.)  in  diameter,  3  miles  long,  and 
offers  40  ohms  resistance.     A  second  wire  of  the  same  material  is  50  mils 
in  diameter  and  9  miles  long.     What  is  the  resistance  of  the  latter  ? 
Ans.  76.8  ohms. 

^25.  If  the  terminals  of  a  galvanometer  be  shunted  with  a  resistance  ^ 
that  of  the  galvanometer,  what  part  of  the  total  current  will  the  galva- 
nometer measure  ? 

26.  An  electric  lamp  has  a  resistance  of  50  ohms  ;  it  is  connected  to  a 
street  main  by  leads  of  2£  ohms  resistance.     The  heat  developed  in  the 
leads  is  wasted.   What  portion  of  the  entire  heat  developed  in  the  derived 
circuit  is  wasted  ? 

27.  a.  The  internal  resistance  of  a  voltaic  circuit  is  2  ohms,  and  the 
external  resistance  is  16  ohms  ;  what  portion  of  the  entire  heat  developed 
in  the  circuit  is  generated  in  the  battery  ?    b.  If  the  external  resistance 
of  this  circuit  be  reduced  to  .5  ohm,  the  heat  generated  in  the  battery 
will  be  what  part  of  the  total  heat  developed  in  the  circuit  ? 

28.  What  is  the  strength  of  a  current  which  deposits  .02  gram  of 
copper  per  minute  ? 

29.  Suppose  that  there  are  a  number  of  cells  joined  in  series  but  the 
circuit  is  completed  by  short,  thick,  copper  leading  wires  of  practically  no 
resistance,  would  any  advantage  be  gained  by  adding  thereto  more  cells 
in  series  ?     Explain. 

30.  A  battery  of  20  cells  is  divided  into  four  groups.     Each  group 
consists  of  five  cells  connected  in  series,  and  the  four  groups  are  con- 
nected in  multiple  arc.     Compare  the  E.M.F.  and  the  resistance  of  this 
battery  with  that  of  a  single  cell. 

31.  What  E.M.F.  of  a  dynamo  generator  will  be  necessary  to  maintain 
a  12-ampere  current  for  100  arc  lamps  in  series,  each  of  which  has  a 
resistance  of  5  ohms,  the  resistance  of  the  line  wire  being  20  ohms,  and 
the  dynamo  resistance  being  25  ohms  ? 


CUKRENT,  RESISTANCE,  POTENTIAL    DIFFERENCE.     517 


SECTION  XII. 


VERIFICATION    OF    OHM  S    LAW. 

484.    Relation  of  current,  resistance,  and  potential  difference. 

This  relation  is  best  understood  by  the  aid  of  the  hydraulic 
analogue.  B  (Fig.  399)  represents  a  tank  in  which  water  is  main- 
tained at  a  fixed  level  by  means  of  a  pump  (battery),  while  the 
tank  discharges  through  a  pipe  (conductor)  N  O.  At  equal  inter- 
vals glass  tubes,  serving  as  manometers  (potential  meters),  rise 
from  the  discharge  tube.  The  hight  to  which  the  water  rises  in 
each  tube  indicates  the  pressure  at  that  point.  The  pressure  falls 
off  uniformly  toward  0,  as 
indicated  by  the  dotted 
line  "as.  The  pressure  of 
the  column  a'  a  is  required 
to  force  the  current  against 
the  resistance  of  the  pipe 
N  O.  The  force  urging  the 


water  from 
the  pipe  is 
of  pressure 
This  might 


a'  to  &'  along 
the  difference 
at  a'  and  &'. 
be  called  the 


FIG.  399. 


water  motive-force  between 
a'  and  b'.  If  of  e'  be  four 
times  d'e',  the  resistance 
will  be  four  times  as  great 
and  the  water-motive  force 
between  a"  and  e'  will  be 

four  times  as  great  as  that  between  d'  and  e'.  The  fall  of  pressure 
is  the  same  for  each  unit  of  resistance.  These  facts  in  hydraulics 
have  their  exact  parallel  in  the  case  of  electric  flow,  and  the 
analogues  are  too  apparent  to  require  rehearsal.  The  fact  to  be 
established  is  that  every  current  is  due  to  a  determinable  E.M.F. 
in  the  circuit,  and  fractional  parts  of  the  circuit  require  fractional 
parts  of  the  total  E.M.F.  The  portion  of  the  total  E.M.F.  exerted 
in  forcing  the  current  through  any  section  of  the  circuit  is  in  exact 
proportion  to  the  relative  resistance  of  such  section.  For  example, 
a  battery  of  ten  units  resistance  may  supply  an  outer  circuit  of  ten 
units  resistance;  then  one-half  of  the  E.M.F.  will  be  exerted 
against  battery  resistance,  and  one-half  against  external  resistance. 


518 


ETHER    DYNAMICS. 


If  the  same  battery  supply  a  line  of  1000  units  resistance,  the 
energy  expended  in  the  outer  circuit  is  about  T9^  of  the  total 
energy.  The  electrical  efficiency  of  an  electric  generator  is  the 
resistance  of  the  outer  circuit  divided  by  the  total  resistance.  In 
the  example  above  the  efficiency  of  the  battery  is 
1000 


1000  +  10 ' 
485.    Expenditure  of  eneryg. 


or  about 


FIG.  400. 


The  relative  resistances 
of  conductors  carrying  con- 
stant currents  define  the 
relative  expenditure  of  en- 
ergy upon  such  conductors. 
The  energy  may  appear  as 
heat,  as  mechanical  work, 
or  as  that  of  chemical 
decomposition.  The  work 
done  is  due  to  the  current 
and  to  a  fall  of  potential 
along  a  conductor,  and  the 
fall  is  determined  by  the 
relative  resistances. 

This  subject  may  be  il- 
lustrated graphically  thus : 
Let  the  line  A  B  (Fig.  400) 
represent  the  length  of  a 
circuit  (say  1000  ft.),  and 
the  line  A  C  the  total  fall 
of  potential ;  then  obvious- 
ly the  slope  of  the  line 
CB  will  represent  the 
average  rate  of  fall  of  po- 
tential throughout  the  cir- 
cuit. But  suppose  that 
the  line  for  equal  lengths 
of  the  conductor  varies  in 
resistance.  Thus  assume 
that  one-tenth  the  resist- 
ance and  consequently  one- 
tenth  the  fall  of  potential 
(Cd)  is  included  in  the 


EXPENDITURE    OF    ENERGY. 


519 


first  quarter  (A a),  or  250  feet;  then  that  the  next  250  feet  (a 6, 
being  very  fine  wire,  perchance)  represents  one-half  the  total  resist- 
ance; the  next  250  feet  (be)  represents  one-fourth  the  total  resist- 
ance; and  the  remaining  resistance,  fifteen-hundredths,  is  in  the 
last  section  (c  B)  of  250  feet.  Then  the  lines  C  a',  a'  &',  U  c',  and 
c'  B  represent  respectively  the  rate  of  fall  of  potential  in  each  sec- 
tion of  250  feet.  The  fall  in  each  section  is  proportional  to  the 
resistance,  and  again  to  this  is  proportional  the  work  performed  by 
the  current  in  each  section. 

The  above  facts  may  be  verified  experimentally  as  follows  :  P  Q 
(Fig.  401)  is  a  fine  German-silver  wire  one  meter  long,  stretched 
along  a  board  over  a  metric  scale ;  B  is  a  battery  ;  G,  a  mirror 
galvanometer ;  K,  a  key  for  closing  the  circuit ;  and  R  a  coil  of 
German-silver  wire  of  high  resistance.  When  the  free  end  of  the 
wire,  S,  is  applied  to  any 
point  of  the  wire  P  Q,  the 
circuit  is  shunted  through 
G  and  R.  By  this  means 
an  extremely  small  por- 
tion of  the  current  will  be 
shunted  through  the  gal- 
vanometer. This  will  not 
perceptibly  change  the  po- 
tentials of  the  points  P  and 
S.  Observations  are  made 
by  placing  the  free  end  of  FlG  ^ 

the  wire,   S,   at   different 

points  along  the  wire  and  reading  the  deflection  produced  at  each 
point.  Now  if  the  potential  differences  are  proportional  to  the 
resistances,  i.e.  to  the  lengths  of  wire  between  the  points  P  and  S, 
it  follows  that  this  resistance  should  have  a  constant  ratio  to  the 
difference  of  potential  between  the  same  points.  But  the  difference 
of  potential  is  expressed  by  the  current  which  it  sends  through  the 
galvanometer,  so  that  this  current  (which  is  indicated  by  the  deflec- 
tion of  the  galvanometer  needle)  should  be  proportional  to  the 
distance  between  P  and  S. 

E.M.F.  of  a  battery.  The  E.M.F.  of  a  battery  is  considered  to 
be  the  difference  of  potential  between  its  poles  when  the  circuit  is 
open.  If  the  circuit  be  closed,  the  difference  of  potential  at  its 
poles  will  depend  on  the  resistance  of  the  conductor  connecting 
them.  In  this  case  it  is 


520  ETHER    DYNAMICS. 

V  -    ER    (See  §  475} 

in  which  E  is  the  E.M.F.  of  the  battery,  R  the  external  resistance, 
and  r  the  battery  resistance.  From  this  it  follows  that  (1)  the 
difference  of  potential  at  the  poles  of  the  battery  is  less  when  the 
circuit  is  closed  than  when  it  is  open  ;  (2)  it  is  less  with  a  small 
than  with  a  large  external  resistance  ;  and  (3)  it  is  greater  with  a 
small  than  with  a  large  internal  resistance. 

SECTION   XIII. 

MAGNETS    AND    MAGNETISM. 

486.  Laiv  of  magnets.1  —  Suspend  by  fine  threads  in  a 
horizontal  position  two  stout  darning-needles  which  have 
been  drawn  in  the  same  direction  (e.g.  from  eye  to  point) 
several  times  over  the  same  pole  of  a  powerful  electro-magnet. 
These  needles,  separated  a'  few  feet  from  each  other,  take 
positions  parallel  with  each  other,  and  both  lie  in  a  northerly 
and  southerly  direction  with  the  points  of  each  turned  in  the 
same  direction. 

That  point  in  the  Arctic  zone  of  the  earth  towards  which 
magnetic  needles  point  is  called  the  north  magnetic  pole  of 
the  earth.  That  end  of  a  needle  which  points  toward  the 
north  magnetic  pole  of  the  earth  is  called  the  north-seeking, 
marked,  or  -\- pole  ;  this  is  the  end  that  is  always  marked  for 
the  purpose  of  distinguishing  one  from  the  other.  That  end 
of  the  needle  which  points  southward  is  called  the  south- 
seeking,  unmarked,  or  — pole. 

Experiment  1.  —  Bring  both  points  near  each  other  ;  there  is  a  mutual 
repulsion.  Bring  both  eyes  near  each  other  ;  there  is  a  mutual  repulsion. 
Bring  a  point  and  an  eye  near  each  other ;  there  is  a  mutual  attraction. 

1  The  word  magnet  is  supposed  to  have  been  derived  from  the  name  of  an  ancient 
district  in  Asia  Minor  called  Magnesia,  where  was  discovered  at  an  early  period  a 
mineral  (now  known  as  the  magnetic  oxide  of  iron)  which  possesses  the  property  of 
attracting  iron.  The  term  lodestone,  or  "  leading  stone  "  (inasmuch  as  it  takes  a 
definite  position  north  and  south)  has  been  given  to  these  natural  magnets. 


MAGNETIC    TRANSPARENCY    AND    INDUCTION.        521 

Like  poles  of  magnets  repel,  unlike  poles  attract  each  other. 

487.    Magnetic  transparency  and  induction. 

Experiment  2.  —  Interpose  a  piece  of  glass,  paper,  or  wood-shaving 
between  the  two  magnets.  These  substances  are  not  themselves  per- 
ceptibly affected  by  the  magnets,  nor  do  they  in  the  least  affect  the 
attraction  or  repulsion  between  the  two  magnets. 

Substances  that  are  not  susceptible  to  magnetism  are  said 
to  be  magnetically  transparent.  When  a  magnet  causes  another 
body,  in  contact  with  it  or  in  its  neighborhood,  to  become  a 
magnet,  it  is  said  to  induce1  magnetism  in  that  body.  As 
attraction,  and  never  repulsion,  occurs  between  a  magnet  and 
an  unmagnetized  piece  of  iron  or  steel,  it  must  be  that  the 
magnetism  induced  in  the  latter  is  such  that  opposite  poles 
are  adjacent  ;  that  is,  a  N  or  +  pole  induces  a  S  or  —  pole 
next  itself,  as  shown  in  Fi<*  402. 


FIG.  402. 

488.  Polarity. 

Experiment  3.  —  Strew  iron  filings  on  a  flat  surface,  and  lay  a  bar 
magnet  on  them.  On  raising  the  magnet  it  is  found  that  large  tufts  of 
filings  cling  to  the  poles,  as  in  Fig.  403,  especially  to  the  edges  ; 
but  the  tufts  diminish  regularly  in  size  from  each  pole  towards 
the  center,  where  none  are  found. 

Magnetic  attraction  is  greatest  at  the  poles,  and 
diminishes  towards  the  center,  where  it  is  nothing  ;  i.e. 
the  center  of  the  bar  is  neutral.  This  dual  character 
of  the  magnet,  as  exhibited  at  the  opposite  extremi- 
ties of  a  magnet,  is  called  polarity.  If  a  magnet  be 
broken,  each  piece  becomes  a  magnet  with  two  poles 
and  a  neutral  line  of  its  own. 

489.  Retentivity  and  resistance. 

It  is  more  difficult  to  magnetize  steel  than  iron  ; 
on  the  other  hand,  it  is  difficult  to  demagnetize  steel,  ] 

1  A  word  first  vaguely  used  by  Faraday  in  the  sense  of  Influence. 


522  ETHER   DYNAMICS. 

while  soft  iron  loses  nearly  all  its  magnetism  as  soon  as  it  is 
removed  from  the  influence  of  the  inducing  body.  That 
quality  of  steel  by  which  it  resists  the  escape  of  magnetism 
which  it  has  once  acquired  is  called  its  retentivity.  The 
greater  the  retentivity  of  a  magnetizable  body,  the  greater  is 
the  resistance  which  it  offers  to  becoming  magnetized.  The 
harder  steel  is,  the  greater  is  its  retentivity.  Hence,  highly 
tempered  steel  is  used  for  permanent  magnets.  Hardened 
iron  possesses  considerable  retentivity  ;  hence  the  cores  of 
electro-magnets  should  be  made  of  the  softest  iron,  that  they 
may  acquire  and  part  with  magnetism  instantaneously. 

490.  Forms  of  artificial  magnets.  —  Artificial  magnets,  in- 
cluding permanent  magnets  and  electro-magnets,  are  usually 
made  in  the  shape  either  of  a  straight  bar  or  of  the  letter  U, 
according  to  the  use  to  be  made  of  them.  If  we  wish,  as  in 
the  experiments  already  described,  to  use  but  a  single  pole, 
it  is  desirable  to  have  the  other  as  far  away  as  possible; 
then,  obviously,  the  bar  magnet  is  most  convenient.  But  if 
the  magnet  is  to  be  used  for  lifting  or  holding  weights,  the 
U-form  is  far  better,  because  the  attraction  of  both  poles 
is  conveniently  available.  Magnets,  when  not  in  use,  ought 
always  to  be  protected  by  armatures  (A,  Fig.  404)  of  soft 
iron ;  for,  notwithstanding  the  retentivity  of 
steel,  they  slowly  part  with  their  magnetism. 
But  when  an  armature  is  used,  the  opposite  poles 
of  the  magnet  and  armature  being  in  contact 
with  each  other,  i.e.  N  with  S,  they  serve  to  bind 
each  other's  magnetism.  Thin  bars  of  steel  can 
be  more  thoroughly  magnetized  than  thick  ones. 
Hence,  if  several  thin  bars  (Fig.  404)  be  laid  side 
by  side,  with  their  corresponding  poles  turned  in 
FIG.  404.  tne  same  direction  and  then  screwed  together,  a 
very  powerful  magnet  is  the  result.  This  is  called  a  com- 
pound magnet. 


MAGNETIC    LINES    OF   FORCE. 


523 


SECTION   XIV. 

MAGNETIC    LINES    OF    FORCE.       THE    MAGNETIC    CIRCUIT. 

491.    Magnetic    lines    of  force.  —  These    lines    are    easily 
studied  by  the  use  of  iron  filings.     The  field  of  force  around 

a  magnet  is  shown      lf^tl^r^^rr^m^^_^^r^. »_^__. 

by  placing  a  paper 
over  it,  dusting 
filings  upon  the 
paper,  and  tapping 
it.  The  filings 
take  symmetrical 
positions,  form 
curves  between  the 
poles  of  the  mag- 
net or  magnets, 
and  show  that  the 
lines  of  force  con- 
nect the  opposite 
poles  of  the  mag- 
net. The  fact  is,  that  each  filing,  when  brought  within  the 
influence  of  the  magnetic  field,  becomes  a  magnet  by  induc- 
tion, and  of  necessity  tends  to  take  a  definite  position  which 


FIG.  405. 


\  \\N 


\h 


FIG.  406, 


524 


ETHER    DYNAMICS. 


represents  the  resultant  of  the  forces  acting  upon  it  from 
each  pole  of  the  system.  Fig.  405  represents  a  magnetic 
field  photographed  from  a  specimen  paper,  and  Fig.  406  is  a 


FIG.  407. 

graphical  representation  of  the  same.  In  this  illustration 
the  unlike  poles  of  two  magnets  are  placed  opposite  each 
other.  Fig.  407  is  a  diagram  of  paths  of  lines  of  force  of  a 
bar  magnet,  arid  Fig.  408  of  a  horseshoe  magnet. 

492.  Magnetic  circuit. — A  line  of 
force  is  assumed  arbitrarily  to  start 
from  the  N-pole  and  to  pass  through 
the  surrounding  medium  (e.g.  the  air), 
entering  the  magnet  by  the  S-pole, 
and  completing  its  path  through  the 
magnet  itself  to  its  starting-point 
(the  N-pole),  thus  forming  a  complete 
circuit  (Fig.  407).  These  lines  do 
not  all  emerge,  however,  from  the 
extremities.  A  multitude  of  lines 
start  from  all  parts  of  the  magnet 
and  enter  at  corresponding  points  on 
the  other  side  of  its  central  or  neutral 
line.  No  magnetic  line  of  force  can  exist  without  completing 


FlG.  408. 


LINE    OF    FORCE   THE    AXIS    OF    ETHER    WHIRLS.       525 


its  own  circuit/  and  lines  of  force  never  cross  or  merge  into 
one  another,  consequently  a  magnet  cannot  have  a  single  pole. 
Lines  of  force  possess  several  peculiar  characteristics.  One 
is  that  in  air  and  most  other  mediums  they  tend  to  separate 
from  one  another,  but  at  the  same  time  tend  to  become  as 
short  as  possible.  The  strain  is  as  if  these  lines  were 
stretched  elastic  threads  endowed  with  the  property  of  repel- 
ling one  another  as  well  as  of  shortening  themselves  ;  in 
other  words,  there  is  tension  along  the  lines  and  pressure  at 
right  angles  to  them.  Air  is  a  poor  conductor  for  lines  of 
force,  or  its  permeability2  is  low  ;  on  the  other  hand,  iron 
has  high  permeability  for  lines  of  force,  and  if  a 
piece  of  iron  be  brought  within  a  magnetic  field,  a 
portion  of  the  lines  of  force  will  crowd  together 
into  it,  leaving  their  normal  paths  through  the  air 
for  a  medium  of  greater  permeability. 

493.    Line  of  force  the  axis  of  ether  whirls. 

A  line  of  force  is  supposed  to  represent  the  axis  of 
a  series  of  ether  whirls.  Fig.  409  gives  a  crude  pic- 
torial representation  of  the  supposed  constitution  of 
the  whirls  of  an  electro-magnetic  line  of  force.  A 
series  of  curtain  rings  might  be  strung 
upon  a  stretched  thread  and  caused  to 
rotate  around  it.  This  would  give  some 
idea  of  the  hypothesis;  the  thread 
would  give  the  direction  of  the  line  of 
force  and  its  conventional  representa- 
tion as  a  simple  line.  The  perfectly  cir- 
cular line  of  force  is  such  as  those  (§  445) 
surrounding  a  wire  carrying  a  current, 
and  represented  in  Fig.  410.  Its  mechanical  analogue 
is  seen  in  a  smoke-ring  such  as  is  sometimes  caused  to 


FIG.  410. 


FIG.  409. 


1  Herein  exists  a  notable  difference  between  these  and  electrostatic  lines  of  force. 
Every  electrostatic  charge  is  bound,  i.e.  has  an  opposite  and  equal  charge  somewhere. 
To  this  its  lines  of  force  go  ;  but  there  is  no  circuit,  there  is  only  a  connection. 

2  Permeability  is  a  quality  christened  by  Lord  Kelvin. 


526  ETHER    DYNAMICS. 

rise  from  the  bowl  of  a  tobacco  pipe  by  skillful  operation.  It  is 
well  illustrated  by  the  rings  arising  from  the  spontaneous  combus- 
tion of  phosphureted  hydrogen  in  air.  These  show  the  whirling, 
rotary  motion  around  the  circular  axis  of  the  ring.  Such  are  called 
vortex  rings. 

494.   Attraction  and  repulsion  between  magnetic  poles. 

The  tendency  of  these  whirls  is  to  bulge  out  by  reason  of  centri- 
fugal force.  An  assemblage  of  such  parallel  whirls  would  compress 
each  other  laterally  and  cause  a  longitudinal  tension  (§  425).  On 
this  hypothesis  the  phenomena  of  magnetic  attraction  and  repulsion 
are  explainable. 

If  the  N-pole  of  one  magnet  be  placed  opposite  the  S-pole 
of  another  (Fig.  406),  the  lines  of  force  issuing  from  the 
former  will  enter  the  latter,  and,  tending  to  shorten,  will 
produce  attraction.  If  the  similar  ends  be  opposed  (Fig.  411), 


FIG.  411. 


the  lines  of  force  will  be  turned  away  from  each  pole  in  all 
directions,   and  will  complete  their  circuits    independently. 
Thus   becoming   parallel   they   will    repel   one  another;  for 
this  reason  like  magnetic  poles  repel  each  other. 
495.    Equipotential  surfaces. 

(The  potential  at  any  point  in  a  magnetic  field  is  the  quantity  of 
work  that  would  have  to  be  done  in  bringing  a  +  unit  of  magnetism 
from  an  infinite  distance  to  that  point. 

If  a  magnetized  particle  be  moved  either  toward  or  from  a  mag- 
netic pole,  work  is  done  either  by  or  against  the  attracting  or  re- 
pelling force,  and  the  particle  is  said  to  be  moved  from  a  point 
where  the  magnetic  potential  has  one  value  to  a  point  where 


TUBES    OF   FORCE. 


527 


another  value.  Imagine  an  N-pole  isolated  from  its  companion 
S-pole.  We  may  suppose  that  all  points  at  equal  distances  from 
this  pole  are  at  the  same  potential,  and  these  points  joined  form  a 
spherical  surface.  The  potential  at  every  point  of  this  surface 
(being  the  same)  may  be  represented  by  V.  Within  and  without 
this  lie  successive  spherical  equipotential  surfaces  over  each  of  which 
the  potential  is  constant,  but  the  potential  at  each  surface  differs 
from  that  at  any  of  the  others.  No  work  is  required  to  move  a 
quantity  of  magnetism  from  one  point  on  an  equipotential  surface 
to  another  point  on  the  same  surface.  Equipotential  surfaces  are 
not  necessarily  spherical.  But  whatever  be  their  form,  the  lines  of 
force  are  always  at  right  angles  to  the  equipotential  surfaces. 

496.    Tubes  of  force. 

Suppose  A  B  (Fig.  412)  to  be  a  section  of  an  equipotential  surface. 
Lines  of  force  pass  through  the  surface,  those  grazing  its  edges  cut- 
ting off  an  area,  A'  B',  from  another  equipotential  surface.     The 
space  comprised  between  these  equi- 
potential areas  and  bounded  laterally 
by  lines  of  force  is  called  a  tube  of 
force.     This  space  may  be  supposed 
to  be  filled  with  a  bundle  of  lines  of 
force.      Now  the   intensity    of    the 
magnetic  force  at  the  potential  A'  B', 
as  compared  with  that  at  A  B,  is  in 
inverse  proportion  to  the  magnitudes 
of  their  respective  areas. 

The  intensity  of  magnetic  forces 
at  any  two  points  may  be  compared 
by  stating  the  relative  numbers  of 
the  lines  of  force  which  pass  through 
equal  units  of  area  of  the  equipoten- 
tial surfaces  containing  the  points 
compared.  The  fewer  these  lines  per  unit  area,  the  less  the  local 
intensity  of  the  force.  The  strength  of  field  between  the  poles  of  a 
magnet  may  be  expressed  in  dynes,  but  now  it  is  more  common 
among  electricians  to  express  this  strength  by  the  number  of  lines 
of  force  per  cm2,  each  line  of  force  representing  a  dyne. 

For  example,  if  the  strength  of  the  magnetic  field,  or  the  force 
on  a  unit  pole,  be  ten  dynes  at  any  point,  then  ten  lines  of  force  are 


FIG.  412. 


528 


ETHER    DYNAMICS. 


said  to  pass  through  an  area  of  1  cm-  held  perpendicularly  to  these 
lines. 

497.    Strength  of  magnetic  field  by  the  method  of  oscillations. 

This  method  of  comparing  the  strength  of  the  magnetic  field  at 
different  points  in  it  depends  on  the  principle  that  a  pendulum 
makes  isochronous  oscillations  when  the  length  of  the  arc  is  very 
small,  and  that  the  force  which  is  always  pulling  it  back  to  its 
position  of  rest  is  proportional  to  the  square  of  the  number  of  oscil- 
lations in  a  given  time. 

A  magnetic  needle  about  3  in.  long  is  suspended  by  a  silk  fiber 
in  the  magnetic  meridian.  The  needle  is  deflected  from  the  merid- 
ian and  allowed  to  vibrate,  and  the  number  of  vibrations  made  in 
a  given  time  are  counted.  Suppose  that  11  oscillations  be  made 
in  30  seconds  under  the  action  of  the  earth.  If  E  represent  the 
strength  of  the  earth's  magnetic  field,  then  E  may  be  measured  by 
II2  =  121. 

Then  on  placing  a  long  bar  magnet  (Fig.  413)  in  a  vertical  position 
in  the  same  meridian  with  the  needle,  and  its  N-pole  opposite  the 
S-pole  of  the  needle,  the  two  poles  being  4  cm  apart, 
suppose  that  the  number  of  oscillations  made  in  30 
seconds  be  51.  If,  then,  M4  represent  the  intensity 
of  the  field  at  a  distance  of  4  cm,  E  +  M4  is  measured 
by  512  =  2601.  Hence  M4  is  measured  by  2601  —  121 
=  2480. 

Suppose  that  on  removing  the  pole  to  a  distance 
of  8  cm  the  number  of  oscillations  is  27.  Denoting 
by  Mg  the  intensity  of  the  field  of  the  magnet  at  a 
distance  of  8  cm,  we  have  E  +  MS  measured  by  272  = 
729,  and  therefore  M8  is  measured  by  729  —  121  = 
608.  Hence  M4  :  M8  =  2480  :  608  =  4  :  1  (within  the 
FIG.  413.  limit  of  errors  of  observation). 

498.  Laiv  of  inverse  squares.  —  In  this  manner  may  be 
demonstrated  experimentally  the  Law  of  Inverse  Squares  as 
applied  to  magnetism,  viz.  :  The  force  exerted  between  two 
magnetic  poles  varies  inversely  as  the  square  of  the  distance 
between  them. 

The  magnitude  of  the  force  in  any  case  is  numerically  equal 


DEFINITIONS.  529 

to  the  product  of  the  strength  of  the  poles  divided  by  the  square 
of  the  distance  between  them ; 

m  m1 

S  =  '~~d^' 

The  C.G.S.  unit  pole  is  that  pole  which  repels  an  equal  pole 
placed  a  centimeter  away  with  a  force  of  one  dyne.1 

499.  Definitions.  —  We  are  now  in  a  position  to  understand 
the  following  definitions  :  A  portion  of  space  throughout  which 
magnetic  effects  are  exerted  by  a  distribution  of  magnetism  is 
called  a  magnetic  field.  At  each  point  of  the  field  a  pole  of 
intensity,  m,  is  acted  on  by  a  definite  force.  The  intensity 
of  a  magnetic  field  at  a  given  point  is  equal  to  the  force  in 
dynes  with  which  a  unit  pole  would  be  acted  upon  at  that 
point.  Let  H  denote  the  intensity  of  field  at  any  point ; 
then  the  force  actually  exerted  at  that  point  on  a  pole  of 
strength  m  is  m  H. 

A  line  of  magnetic  force  is  a  line  drawn  in  such  a  manner 
that  the  tangent  to  it  at  each  point  is  in  the  direction  of  the 
resultant  magnetic  force  at  that  point. 

The  magnetic  potential  at  any  point  is  the  work  that  must 
be  done  against  the  magnetic  forces  in  bringing  up  a  unit 
magnetic  pole  from  a  point  at  an  infinite  distance  to  the 
given  point.  The  difference  of  magnetic  potential  between 
two  points  in  the  field  is  the  work  done  in  transferring  a  unit 
magnetic  pole  from  one  of  these  points  to  the  other,  against 
magnetic  forces.  A  surface  in  which  the  magnetic  potential 
at  all  its  points  is  the  same  is  an  eqidpotential  surface. 

Let  m  be  the  quantity  of  magnetism  at  one  of  the  poles  of 
a  magnet,  and  I  the  distance  between  the  poles 2 ;  the  magnetic 
moment  of  the  magnet  is  the  product  m  I. 

1  In  practice  it  is  impossible  to  obtain  a  single  isolated  pole  ;  the  total  quantity  of 
(+  and  — )  magnetism  in  any  magnet  is,  algebraically  reckoned,  zero. 

2  In  a  steel  bar  magnet  the  poles  are  not  strictly  at  the  extremities,  and  hence 
the  magnetic  length  is  a  little  less  than  the  actual  length  of  the  magnet.    For  most 
bar  magnets,  the  magnetic  length  is  about  .83  of  the  actual  length.    The  magnetic 
length  of  a  horse-shoe  magnet  is  the  shortest  distance  between  its  poles. 


530  ETHER    DYNAMICS. 

The  intensity  of  magnetization  is  the  ratio  of  the  magnetic 
moment  of  a  magnet  to  its  volume. 

A  magnetizable  body  placed  in  a  magnetic  field  becomes 
magnetized  in  the  direction  of  the  lines  of  force  of  the  field. 
Its  magnetism  is  called  induced  magnetism,  and  the  action 
itself  is  called  magnetic  induction.  The  magnetism  retained 
by  a  magnetic  body  after  it  has  been  withdrawn  from  the 
field  is  called  residual  magnetism. 


SECTION  XV. 

TERRESTRIAL    MAGNETISM. 

500.    The  earth  a  magnet. 

A  dipping-needle  is  so  supported  that  it  can  revolve  in  a  vertical 
plane.  Indifferent  equilibrium  is  first  established  in  the  steel 
needle,  so  that  if  placed  in  a  horizontal  (or  any  other)  position  it 
will  rest  in  that  position.  Then  it  is  strongly  magnetized.  After- 
ward it  will  take  the  horizontal  position  only  at  the  magnetic 
equator  of  the  earth. 

Experiment  1.  —  Place  a  dipping-needle  over  the  +  pole   of    a   bar 

magnet  (Fig.  414).     The  needle  takes  a  vertical  position  with  its  —  pole 

down.     Slide  the  supporting  stand  along  the  bar ;  the  —  pole  gradually 

rises  until  the  stand  reaches 
the  middle  of  the  bar, 
where  the  needle  becomes 
horizontal.  Continue  mov- 
ing the  stand  toward  the 

N  -  poifl  of  the  bar;   after 

FlG  414  passing  the  middle  of  the 

bar  the  +  pole  begins  to 

dip,  and  the  dip  increases  until  the  needle  reaches  the  end  of  the  bar, 

when  the  needle  is  again  vertical  with  its  +  pole  down. 

If  the  same  needle  be  carried  northward  or  southward  along  the 

earth's  surface,  it  will  dip  in  the  same  way  as  it  approaches  the  polar 

regions,  and  be  horizontal  only  at  or  near  the  equator. 


MAGNETIC    POLES    OF    THE    EARTH. 


531 


Experiment  2.  —  Support  a  small  pane  of  window  glass  on  a  table,  by 
placing  under  the  glass  near  its  corners  four  slices  of  cork  about  one- 
eighth  of  an  inch  thick.  Be- 
neath the  center  of  the  glass 
on  the  table  place  a  circular 
disk  of  magnetized  steel.  Sift 
iron  turnings  upon  the  upper 
face  of  the  glass  through  a 
fine  wire  sieve.  Gently  tap 
the  glass  at  convenient  points 
with  the  end  of  a  lead-pencil. 
The  filings  arrange  themselves 
in  lines  radiating  from  each 
pole. 

Experiment  3.  —  Suspend 
a  small  magnetized  cambric 
needle  by  a  fine  thread  at  its 
center  and  carry  it  around 
the  disk  (Fig.  415).  The 
needle  passes  through  all  the 
phases  stated  in  Exp.  1,  so  FlG  415 

that  we  may  fancy  the  disk 

to  be  the  earth,  and  study  therefrom,  in  a  general  way,  the  changes 
that  the  needle  undergoes,  as  it  is  carried  around  the  earth  in  a  norther- 
ly or  southerly  direction. 


The  last  experiment  presents  a  true  exhibition,  on  a  small 
scale,  of  what  the  earth  does  on  a  large  one,  and  thereby 
presents  one  of  many  phenomena  which  lead  to  the  conclu- 
sion that  the  earth  is  a  magnet.  In  other  words,  these 
phenomena  are  just  what  we  should  expect  if  a  huge  magnet 
were  thrust  through  the  axis  of  rotation  of  the  earth,  as 
represented  in  Fig.  416,  —  having  its  N-pole  near  the  S  geo- 
graphical pole,  and  its  S-pole  near  the  N  geographical  pole ; 
or  if  the  earth  itself  were  a  magnet. 

501.  Magnetic  poles  of  the  earth.  —  It  will  be  seen  that 
there  are  two  points  where  the  needle  points  directly  to  the 
center  of  the  disk.  A  point  was  found  on  the  western  coast 


532 


ETHER    DYNAMICS. 


of  Boothia,  by  Sir  James  Koss,  in  the  year  1831,  where  the 
dipping-needle  lacked  only  one-sixtieth  of  a  degree  of  pointing 

directly  to  the 
earth's  center.  The 

-v,  ^     .      .  ^j«- -s.  same  voyager  sub- 

fe.  sequeJy  SLhed 

a  point  in  Victoria 
Land  where  the 
opposite  pole  of 
the  needle  lacked 
only  1°  20'  of 
pointing  to  the 
earth's  center. 

It  will  be  seen 
that,  if  we  call  that 
end  of  a  magnetic 
needle  which 
points  north  the 

FIG.  416. 

JN-pole,    we    must 

call  that  magnetic  pole  of  the  earth  which  is  in  the  northern 
hemisphere  the  S-pole,  and  vice  versa.  (See  Fig.  416.)  Hence, 
to  avoid  confusion,  many  careful  writers  abstain  from  the  use 
of  the  terms  north  and  south  poles,  and  substitute  for  them  the 
terms  positive  and  negative,  or  marked  and  unmarked  poles. 

502.  Variation  of  the  needle.  —  Inasmuch  as  the  magnetic 
poles  of  the  earth  do  not  coincide  with  the  geographical  poles, 
it  follows  that  the  needle  does  not  in  most  places  point  due 
north  and  south.  The  angle  which  the  vertical  plane  through 
the  axis  of  a  freely  suspended  needle  makes  with  the 
geographical  meridian  of  the  place  is  known  as  the  angle  of 
declination.  In  other  words  the  angle  of  declination  is  the 
angle  formed  by  the  magnetic  and  geographical  meridians. 
This  angle  differs  at  different  places.  The  magnetic  axis  of 
a  needle  is  a  straight  line  connecting  its  two  poles. 


ISOGONIC    CURVES. 


533 


Experiment  4.  —  We  can  easily  find,  as  did  Columbus,  the  declination 
at  any  place  by  the  following  method  :  Set  up  two  sticks  so  that  a  string 
joining  them  will  lie  in  the  same  vertical  plane  with  the  Pole  Star  ;  the 
string  will  lie  in  the  geographical  meridian.  Place  a  long  magnetic 
needle  over  the  string ;  the  angle  between  the  needle  and  the  string  is  the 
required  declination.  If  great  accuracy  be  required,  allowance  must  be 
made  for  the  fact  that  the  star  is  not  exactly  over  the  pole,  but  appears 
to  describe  daily  around  it  a  circle  whose  diameter  is  at  the  present  time 
about  2|°. 

503.    Isogonic  curves. — These  are  lines  connecting  all  points 


FIG.  417. 

of  equal  declination  on  the  earth's  surface.  The  line  of  no 
declination  or  isogonic  of  0°  (Fig.  417)  commences  at  the  N. 
magnetic  pole  about  lat.  70°,  long.  96°,  passes  in  a  south- 
easterly direction  across  Lake  Erie  and  Western  Pennsyl- 
vania, and  enters  the  Atlantic  Ocean  near  the  boundary 
between  the  Carolinas.  Pursuing  its  course  through  the 
south  polar  regions,  it  reappears  in  the  eastern  hemisphere 
and  crosses  Western  Australia,  the  Caspian  Sea,  and  thence 
to  the  Arctic  Ocean.  There  is  also  a  detached  line  of  no 
declination  inclosing  an  oval  area  in  Eastern  Asia  and  the 
Pacific  Ocean.  In  the  eastern  (or  Atlantic)  hemisphere, 


534 


ETHER    DYNAMICS. 


M 


bounded  by  the  line  of  no  declination,  the  declination  is 
westward,  as  indicated  by  continuous  lines  in  the  figure. 
In  the  western  (or  Pacific)  hemisphere  the  declination  is 
eastward,  as  indicated  by  dotted  lines. 

The  magnetic  poles  are  not  fixed  objects  that  can  be  located 
like  an  island  or  cape,  but  are  constantly  changing.  They 
appear  to  swing,  something  lifce  a  pendulum,  in  an  easterly 
and  westerly  direction,  each  swing  requiring  centuries  to 
complete  it.  The  north  magnetic  pole  is  now  on  its  westerly 
swing. 

504.  Inclination  or  dip.  — We  have  seen  that  in  the  northern 
hemisphere  the  lines  of  force  tend  downward  and  northward. 

A  magnetic  needle  thus 
tends  to  place  itself  so 
that  its  axis  points  down- 
ward and  to  the  magnetic 
pole  of  the  earth.  The 
angle  which  the  axis  of 
a  freely  suspended  mag- 
netic needle  makes  with 
the  horizontal  plane  is 
called  the  inclination  or 
dip  of  the  needle.  Fig. 
418  represents  a  dipping- 
needle  such  as  is  used 
in  determining  magnetic 
inclination,  and  Fig.  419 
represents  a  declinometer 
for  determining  the  decli- 
nation. A  is  a  mounted 
telescope  for  sighting 
some  astronomical  object,  e.g.  the  north  star.  Its  axis  is 
levelled  by  the  spirit  level  B. 

The    line   passing   in  an   easterly  and  westerly  direction 


FIG.  418. 


INTENSITY. 


535 


FIG.  419. 


around  the  earth  along  which  the  lines  of  force  (or  needle) 
are  horizontal,  i.e.  at  which 
the  dip  is  zero,  is  the  magnetic 
equator.  It  does  not  coincide 
with  the  geographical  equator. 
The  lines  roughly  parallel  to 
the  magnetic  equator,  along 
which  the  dip  is  equal,  are 
the  magnetic  parallels.  These 
are  lines  along  which  equipo- 
tential  surfaces  cut  the  sur- 
face of  the  earth. 

We  have  before  noted  the 
fact  that  lines  of  force  are 
always  at  right  angles  to  equi- 
potential  surfaces,  and  conse- 
quently at  the  magnetic  poles 
where  the  dip  is  90°  the  equipotential  surfaces  are  tangent 
to  the  earth's  surface. 

505.  Intensity.  —  The  force,  expressed  in  absolute  measure, 
with  which  the  earth's  magnetism  urges  a  unit  magnetic  pole 
(§  498)  is  the  intensity  of  the  earth's  magnetic  field l  at  the 
place. 

The  earth's  action  on  a  needle  is  a  mechanical  couple, 
the  effect  of  which  is  to  cause  only  a  rotary  motion.  This 
is  what  is  meant  when  the  earth's  action  on  the  needle  is 
said  to  be  directive  only. 

506.  Connection  between  the  sun  and  the  earth's  magnetism. 

1  If  the  inclination  be  found,  and  the  horizontal  component  of  the  intensity  of 
the  earth's  field  acting  upon  a  unit  pole  be  known,  we  have  the  data  required  for 
determining  by  parallelogram  of  forces  the  whole  intensity  of  the  earth's  magnetic 
field  in  the  direction  of  the  lines  of  force  at  any  point.  Such  a  measurement  is  of 
importance  in  refined  work,  since  it  consists  essentially  in  determining  the  couple 
which  must  be  exerted  by  the  earth's  magnetic  force  on  a  needle  in  order  to  balance 
that  produced  by  the  current.  For  methods  of  determining  these  quantities,  see 
Cumming's  Electricity,  or  any  complete  laboratory  manual. 


536 


ETHER    DYNAMICS. 


Magnetic  storms,  or  disturbances  of  the  earth's  magnetism 
coincident  with  outbreaks  of  sun  spots  and  solar  storms,  point 
to  an  undoubted  connection  or  sympathy  between  the  sun  and 
the  earth's  magnetism  ;  but  of  the  nature  of  this  connection 
our  knowledge  is  as  yet  very  limited. 


SECTION   XVI. 

MAGNETIC     RELATIONS    OF    THE     CURRENT.       ELECTRO-MAGNETS. 

507.  Magnetic  field  due  to  a  circular  current.  —  If  a  wire 
be  bent  into  the  form  of  a  circle  of  about  10  in.  diameter, 
and  placed  vertically  in  the  magnetic  meridian,  and  a  card- 
board be  placed  at  right  angles  to  the  circle  so  that  its  hori- 
zontal diameter  is  coincident  with  the  upper  surface  of  the 
cardboard,  and  a  very  strong  current  be  sent  through  the 
wire  in  the  direction  indicated  by  the  arrow-head  in  the  wire, 
iron  filings  sifted  upon  the  card  will  arrange  themselves  as 
shown  in  Fig.  420.  And  if  a  freely  suspended  test-needle 


FIG.  420. 


be  carried  inside  and  outside  the  circle,  the  several  positions 
taken  by  the  needle,  as  indicated  in  the  figure  by  arrows, 
corroborate  the  directions  of  the  lines  of  force  as  indicated 
by  the  filings. 


MAGNETIC    CURRENT. 


537 


If  the  direction  of  the  current  be  reversed,  the  direction  of 
the  needle  will  be  reversed  wherever  it  may  be  placed. 

The  direction  indicated  by  the  N-pole  of  the  magnetic 
needle  placed  anywhere  in  the  field  is  called  the  positive 
direction  of  the  lines  of  force. 

508.  Magnetic  current.  —  In  fact,  when  a  current  traverses 
a  wire  (or  other  conductor)  lines  of  force  encircle  the  electric 
current  at  right  angles  to  it.1  The  electric  current  and  its 
encircling  lines  of  force  always  co-exist,  and  one  varies  directly 
as  the  other  when  there  is  no  magnetic  substance  near  the 
wire.  The  direction  of  the  encircling  lines  of  force  with 
reference  to  the  electric  current  may  be  illustrated  by  the 
use  of  a  corkscrew.  The  direction  of  the  electric  current 
corresponds  to  the  propul- 
sion of  the  point  of  the 
corkscrew  when  entering 
a  cork,  and  the  direction 
in  which  the  screw  is 
turned  or  the  hand  is 
twisted  in  propelling  it 
corresponds  to  the  direc- 
tion of  the  lines  of  force. 

If  a  circle  of  wire  bear- 
ing a  very  strong  current 
be  freely  suspended  and  a 
pole  of  a  very  strong  bar  magnet  be  presented  to  one  of  its 


Fl«.  421. 


1 "  Every  conducting  wire  is  surrounded  by  a  sort  of  magnetic  whirl.  A  great  part 
of  the  energy  of  the  so-called  electric  current  in  the  Avire  consists  in  these  external 
magnetic  whirls.  To  set  them  up  requires  an  expenditure  of  energy  ;  and  to  main- 
tain them  requires  a  constant  expenditure  of  energy.  It  is  these  magnetic  whirls 
which  act  on  magnets,  and  cause  them  to  set,  as  galvanometer  needles  do,  at  right 
angles  to  the  conducting  wire."  —  S.  P.  THOMPSOX. 

It  may  be  demonstrated  that  a  law  analogous  to  Ohm's  Law  is  applicable  to  the 
magnetic  whirl  or  "flux."  Let  C^the  strength  of  the  magnetic  flux  (or  field) 
expressed  in  lines  of  magnetic  force  ;  M  =  the  force  which  gives  rise  to  the  magnetic 
flux,  called  the  magneto-motive  force;  and  B  =  the  resistance  to  the  magnetic  flux  ; 
thenC^M. 


538 


ETHER   DYNAMICS. 


faces,  the  circle  will  be  attracted  or  repelled  according  to  the 
nature  of  the  pole  and  the  direction  of  the  current.  We  may 
consider  a  circular  current  as  if  it  were  a  very  short  magnet, 
one  face  of  the  circle  being  the  north  end,  and  the  other  face 
the  south  end,  as  represented  in  Fig.  421. 

Observe  (Fig.  420)  that  the  directions  of  the  filings  near 
the  center  of  the  circle  lie  nearly  parallel  with  its  axis,  but 
outside  to  the  right  and  left  of  the  axis  the  filings  lie  in 
curves  around  each  wire. 

509.  Solenoid.  —  An  insulated  wire  wound  into  a  helix  of 
considerable  length  as  compared  with  its  diameter  is  called 

a  solenoid.1  It  is  evident 
that  the  intensity  of  the 
magnetic  field  must  be 
greatly  increased  by  the 
joint  action  of  the  many 
current  turns.  The  mag- 
netic field  within  the  sole- 
noid is  nearly  uniform  in 
strength,  and  the  lines  of  force  to  within  a  short  distance  of 
its  ends  are  parallel  with  its  axis,  as  shown  in  Fig.  422.2 

510.  Magnetic  polarity  of  electro-magnetic  solenoid.  —  Fig. 
423  represents  a  small  battery  floating  on  water.     The  lead- 
ing wire  of  the  cell  is 

wound  into  a  horizon- 
tal solenoid.  Slowly 
after  the  cell  is  floated 
it  will  take  a  position 
so  that  the  axis  of 
the  solenoid  will  point 
north  and  south  like  FlG  423 

1  Faraday  first  applied  the  term  solenoid  to  a  system  of  circular  currents  parallel 
with  one  another. 

2  An  open  solenoid  of  a  single  layer  is  here  given,  in  order  the  better  to  show  the 
directions  of  the  several  lines  of  force. 


FlG. 


POLARITY    OF    ELECTRO-MAGNETIC    SOLENOID.       539 


FIG.  424. 


a  magnetic  needle.  Hold  (say)  the  S-pole  of  a  bar  magnet 
near  that  end  of  the  solenoid  which  points  north ;  the  solenoid 
is  attracted  by  the  magnet.  Hold  the  N-pole  of  the  magnet 
near  the  north-pointing  end  of  the  solenoid;  the  magnet 
repels  the  solenoid. 

Eepeat  the  above,  using  in  place  of  the  bar  magnet  another 
solenoid  (Fig.  424);  there  will 
be  a  repetition  of  the  same  phe- 
nomena as  obtained  with  the  bar 
magnet.  Introduce  a  rod  of  soft 
iron  into  the  solenoid  held  in  the 
hand,  thereby  making  of  it  an 
electro-magnet;  the  only  change 
observed  is  that  the  force  of 
attraction  and  repulsion  is  greatly  increased. 

Place  the  wire  of  another  battery  over  and  parallel  with 
the  coil  (Fig.  425),  so  that  the  two  currents  will  flow  in  planes 

at  right  angles  with 
each  other.  The 
coil  is  deflected  like 
a  magnetic  needle 
(Fig.  426). 

Reverse    the   di- 
rection of  the  cur- 
rent above  and  the 
deflection  is  reversed. 

We  thus  prove  that  a  solenoid  bearing  a  current  possesses 
polarity  as  if  it  were  a  magnet,  and  that  there  can  be  pro- 
duced by  a  current-bearing  solenoid  a  magnetic  field  of  the 
same  character  as  that  produced  by  a  permanent  magnet. 
There  is  no  essential  difference  between  a  permanent  magnet, 
a  current-bearing  solenoid,  and  an  electro-magnet,  except  that 
the  last  may  be  made  much  stronger  than  either  of  the 
others. 


FIG.  425. 


FIG.  426. 


540  ETHER    DYNAMICS. 

Given  the  direction  of  the  current  in  a  solenoid,  to  find  the 
N-  and  S-poles  of  the  solenoid,  and  vice  versa. 

RULE  1.     Place  the  palm  of  the  right  hand  against  the  side 
of  the  solenoid  so  that  the  fingers  will  point  in  the  direction 

of  the  current  passing 
through  the  windings 
(as  shown  in  Fig.  427) ; 
the  thumb  will  point  in 
the  direction  of  the  N- 


T      electro-magnet.^ 

RULE  2.      Ascertain 
the  N-pole  of  the  sole- 
noid  or  electro-magnet 
FIG.  427.  ..,  ,.  „ 

with  a  magnetic  needle, 

and  place  the  palm  of  the  right  hand  upon  the  solenoid  so  that 
the  outstretched  thumb  points  in  the  direction  of  the  N-pole  ; 
the  fingers  will  point  in  the  direction  in  which  the  current 
in  the 


SECTION  XVII. 

ELECTRODYNAMICS.        AMPERE'S    THEORY    OF    MAGNETISM. 

511.  Mutual  action  of  currents  on  one  another.  —  We  have 
hitherto  discussed  the  direction  of  the  magnetic  field  due  to 
a  straight  current,  have  determined  the  direction  which  a 
test-needle  takes  in  virtue  of  the  action  of  the  current  field, 
and  have  learned  to  regard  an  electric  current  as  producing 
north  and  south  polarity  along  the  whole  circuit  of  the  cur- 
rent-bearing wire.  That  is,  if  we  suppose  that  a  test-needle 
be  moved  up  or  down  just  back  of  the  current-bearing  wires 

1  The  following  suggestion  will  often  prove  of  practical  value  :  tliat  is  the  south 
pole  of  a  helix  where  the  current  corresponds  to  the  motion  of  the  hands  of  a  watch, 
S^and  that  is  the  north  pole  where  the  current  is  in  the  reverse  direction,*^. 


MUTUAL   ACTION    OF   CURRENTS. 


541 


(Fig.  428),  the  N-  and  S-poles  will  take  the  positions  indi- 
cated by  n  and  s.  We  may  readily  premise  from  inspection 
of  the  polarity  developed,  that  if  the  wires  were  so  sus- 
pended as  to  be  free  to  move  either  toward  or  from  each 
other,  the  pair  of  wires  in  which  the  currents  flow  parallel  to 
each  other  and  in  the  same  direction,  A,  would  attract  each 
other,  and  the  pair  of  wires  in  which  the  currents  flow  in 
opposite  directions,  B,  would  repel  each  other  ;  but  if  the 
currents  be  inclined  to  each  other  as  in  Fig.  429,  they  will 


t  t 

T 


1 1 


s  n 


A  B 

FIG.  428. 


r 


FIG.  429. 


tend  to  move  into  a  position  in  which  they  will  be  parallel 
and  in  the  same  direction.  That  such  actually  takes  place 
may  be  shown  by  the  following  experiments  :  — 

Experiment  1.  —  Fig.  430  represents  a  portion  of  a  divided  circuit. 
The  lower  ends  of  the  wires  dip  about  one-sixteenth  of  an  inch  into 
mercury,  and  the  wires  are  so  suspended  that  they  are  free  to  move  to- 
ward or  from  each  other.  Send  a  current  of  a  battery  of  three  or  four 
Bunsen  cells,  in  multiple  arc,  through  this  divided  circuit.  The  two 
portions  of  the  current  travel  in  the  same  direction  and  parallel  with  each 
other,  and  the  two  wires  at  the  lower  extremities  move  toward  each 
other,  showing  an  attraction. 

Experiment  2.  — Make  the  connections  (Fig.  431)  so  that  the  current 
will  go  down  one  wire  and  up  the  other.  They  repel  each  other. 


542 


ETHER    DYNAMICS. 


Experiment  3.  —  Send  a  current  through  the  spiral  wire  represented 
in  Fig.  432.  Here  the  current  flows  nearly  parallel  with  itself,  and  the 
attraction  causes  the  coil  to  contract  and  to  be  lifted  out  of  the  cup  of 
mercury  below.  But  the  instant  it  leaves  the  mercury  the  circuit  is 
broken,  the  current  and  attraction  cease,  and  the  wire  dips  into  the 
mercury  again.  Thus  rapid  vibratory  motion  of  the  coil  is  produced. 

In  the  experiment  with  the  floating  cell  and  current-bearing 
wire  placed  over  and  parallel  to  the  solenoid  (Fig.  425),  a 
careful  examination  will  disclose  the  fact  that  not  only  da 
the  planes  in  which  the  current  flows  in  the  coil  tend  to 


FIG.  430. 


FIG.  431. 


FIG.  432. 


become  parallel  to  the  current  above,  but  that  the  current  in 
the  upper  half  of  the  coil,  where  the  influence  due  to  prox- 
imity is  greatest,  tends  to  place  itself  so  as  to  flow  in  the 
same  direction  as  that  of  the  current  above. 

512.  Ampere's  Laws.  —  Law  1.  Parallel  currents,  if  in  the 
same  direction,  attract  one  another  ;  and  if  in  opposite  direc- 
tions, they  repel  one  another. 

Law  2.  Currents  that  are  not  parallel  tend  to  become  parallel 
and  flow  in  the  same  direction. 

A  little  reflection  will  show  that  the  observed  motion  is 
the  expression  of  a  tendency  on  the  part  of  any  movable 
current  to  cut  lines  of  magnetic  force  at  right  angles,  the  direc- 


AMPERE'S  THEORY  OF  MAGNETISM.  543 

tion  of  motion  being  reversed  wh'en  the  direction  either  of 
the  lines  of  force  or  of  the  current  is  reversed.  This  prin- 
ciple is  of  immense  importance  from  an  industrial  aspect. 
The  most  important  outcome  of  its  application  is  the  dynamo- 
motor  (§  533)  by  means  of  which  electrical  energy  is  converted 
into  mechanical  energy,  and  through  the  agency  of  which 
electric  street  cars  are  propelled. 

513.  Ampere's  theory  of  magnetism.  —  This  celebrated  theory 
briefly  stated  is  that  magnets  and  solenoid  systems  are  funda- 
mentally the  same;  that  magnetism  is  simply  electricity  in 
rotation,  and  that  a  magnetic  field  is  a  sort  of  whirlpool  of 
electricity.  Not,  of  course,  that  a  steel  magnet  contains  an 
electric  current  circulating  round  and  round  it  as  does  an 
electro-magnet,  but  that  every  molecule  of  iron,  steel,  or 
other  magnetizable  substance  is  the  seat  of  a  separate  current 
circulating  round  it  continuously  and  without  resistance,  and 
thus  every  molecule  is  a  magnet. 

According  to  the  theory,  in  an  unmagnetized  .bar  these 
currents  lie  in  all  possible  planes,  and,  having  no  unity  of. 
direction,  they  neutralize  one  another,  and  so  their  effect 'as 
a  system  is  zero.  But  if  a  current  of  electricity  or  a  magnet 
be  brought  near,  the  effect  of  the  induction  is  to  turn  the 
currents  into  parallel  planes,  and  in  the  same  direction,  in 
conformity  to  Ampere's  Second  Law.  If  the  retentivity  be 
strong  enough,  this  parallelism  will  be  maintained  after  the 
removal  of  the  inducing  cause,  and  a  permanent  magnet  is 
the  result. 

Intensity  of  magnetization  depends  on  the  degree  of  paral- 
lelism, and  the  latter  depends  on  the  strength  of  the  influ- 
encing magnet.  When  these  currents  have  become  quite 
parallel,  the  body  has  received  all  the  magnetism  that  it  is 
capable  of  receiving,  and  is  said  to  be  saturated.  Although 
the  currents  really  circulate  around  the  individual  molecules, 
yet  the  resultant  of  these  forces  is  essentially  the  same  as  if 


544 


ETHER    DYNAMICS. 


N 


FIG.  433. 


a  superficial  sheet  of  currents  circulated  around  the  body  as  a 

whole.  Fig.  433  represents  sections  of  a  cylindrical  magnet,  and 

the  included  circles  represent 
the  circulation  of  the  several 
currents  around  the  mole- 
cules lying  in  these  sections. 
It  will  be  seen  that  the  cur- 
rents at  the  contiguous  sides 
of  any  two  of  these  circles 
move  in  opposite  directions, 
and  therefore  must  neutral- 
ize each  other;  while  the 
currents  that  pass  next  the 

circumference  of  the  magnet  are  not  so  affected. 

514.    Rotation  of  a  magnetic  pole  round  a  current,  and  of 

a  current  round  a  magnetic  pole.  —  A  current  and  a  magnetic 

pole   neither   attract   nor   repel 

each  other,  but  tend  to  rotate 

about    each    other,    the    action 

being  at  right  angles  to  the  line 

joining    them.      Hence    a   mag- 
netic   pole    free    to    move    will 

rotate    round   a   current.      This 

may   be    shown    experimentally 

with  apparatus  like  that  shown 

in  Fig.  434.      The  magnet  NS 

is  bent  so  that  it  may  be  pivoted 

on  its  middle  point,  the  current 

being    brought    to    an    annular 

mercury  cup,  A,  by  means  of  a 

wire  which  dips   into  the  mer- 
cury, leaving  through  the  screw 

cup  B.     When  a  strong  current  is  passing,  the  magnetic  pole 

N  rotates   steadily,  and   by   reversing  the  direction  of   the 

current  the  direction  of  rotation  of  the  pole  is  reversed. 


FIG.  434. 


ROTATION    OF    A    MAGNETIC    POLE. 


545 


The  rotation  of  a  current  round  a  pole  may  be  shown  by 
pivoting  a  wire  bent  in  the  form  of  an  inverted  letter  U  A 
(Fig.  435),  on  the  top  of  a  vertical 
horse-shoe  magnet.  The  divided  current 
passes  through  the  mercury  cups  B  and 
C,  and  leaves  by  the  annular  cups  D  and 
E  which  surround  the  magnet  lower 
down.  The  cups  B  and  C  and  the  wires 
passing  from  them  to  the  cups  D  and  E 
are  so  pivoted  upon  the  extremities  of 
the  magnet  as  to  be  free  to  rotate  around 
its  poles.  When  a  strong  current  is 
passed  through  the  circuit  the  wires  will 
rotate  in  opposite  directions  round  its 
two  poles. 

The  hypothetical  currents  that  circulate  round  a  magnetic 
molecule  we  shall  call  amperian  currents,  to  distinguish  them 
from  the  known  current  that  traverses  the  solenoid.  In 
strict  accordance  with  this  theory,  the  poles  of  the  electro- 
magnet are  determined  by  the  direction  of  the  current  in  the 
helix.  The  inductive  influence  of  the  electric  current  causes 
the  amperian  currents  to  take  the  same  direction  with  itself, 
as  represented  in  Fig.  436. 

By  the  amperian  theory  the  earth's  polarity  is  accounted 


FIG.  435. 


FIG.  436. 


for  by  assuming  it  to  be  girdled  by  electric  currents,  called 
earth  currents,  in  planes  approximately  parallel  to  the  equa- 
tor. A.  person  standing  on  the  Arctic  magnetic  pole  of  the 
earth  would,  if  the  currents  were  visible  to  him,  see  them 


546 


ETHER    DYNAMICS. 


(more  properly  their  resultant,  a  current  sheet)  circulating 
round  him  towards  his  right  from  east  to  west,  or  in  the  same 
direction  as  the  sun  appears  to  him  to  go  round  the  earth. 
According  to  Ampere's  theory  it  is  the  tendency  of  the  nearer 
portions  of  the  earth  currents  and  the  amperian  currents  circu- 
lating round  a  magnetic  needle  to  coincide  in  direction  and  to 
be  parallel ;  that  causes  the  needle  to  point  north  and  south. 
However  well  adapted  this  theory  may  be  to  explain  most 
of  the  known  phenomena  of  magnetism,  it  should  be  borne  in 
mind  that  physicists  of  this  generation  value  the  theory 
rather  as  a  help  to  the  imagination  and  memory,  than  as  a 
true  statement  of  the  facts.  It  is  nearer  the  truth  to  say  that 
the  molecules  are  polarized  as  if  currents  were  circulating 
around  them ;  of  the  actual  existence  of  such  currents  we 
know  nothing.  So  also  of  the  real  nature  of  polarity  we 
know  little  or  nothing. 


SECTION  XVIII. 

ELECTRO-MAGNETIC    INDUCTION. 

515.  Description  of  apparatus.  — A  (Fig.  437)  is  a  short  coil 

of  coarse  wire  (i.e.  the  wire 
which  it  contains  is  com- 
paratively short),  and  has, 
of  course,  little  resistance. 
.B  is  a  long  coil  of  fine  wire 
having  many  turns.  Coil 
A  is  in  circuit  with  two 
Bunsen  cells  in  multiple  arc. 
This  circuit  we  call  the 
primary  circuit,  the  current 
in  this  circuit  the  primary 
or  inducing  current,  and  the 
FlG  437  coil  the  primary  coil.  An- 


DESCRIPTION    OF    APPARATUS. 


547 


other  circuit,  having  in  it  no  battery  or  other  means  of  gener- 
ating a  current,  contains  coil  B  and  a  galvanoscope  with  an 
astatic  needle.1  This  circuit  is  called  the  secondary  circuit, 
the  coil  the  secondary  coil,  and  the  currents  which  circulate 
through  this  circuit  are  called  secondary  or  induced  currents. 

Experiment  1.  —  After  all  the  connections  are  made,  and  a  current  is 
established  in  the  primary  circuit,  and  the  galvanoscope  needle  is  brought 
to  zero,  lower  the  primary  coil  quickly  into  the  secondary  coil,  watching 
at  the  same  time  the  needle  of  the  galvanoscope  to  see  whether  it  moves, 
and,  if  so,  in  what  direction.  Simultaneously  with  this  movement  there 


FIG.  438. 

is  a  movement  of  the  needle,  showing  that  a  current  must  have  passed 
through  the  secondary  circuit.  Let  the  primary  coil  rest  within  the 
secondary,  until  the  needle  comes  to  rest.  After  a  few  vibrations  the 
needle  settles  at  zero,  showing  that  the  secondary  current  was  a  tem- 
porary one.  Now,  watching  the  needle,  quickly  pull  the  primary  coil 
out ;  another  deflection  in  the  opposite  direction  occurs,  showing  that  a 
current  in  the  opposite  direction  is  caused  by  withdrawing  the  coil. 

It  is  evident  that  in  this  case  the  current  does  not  by  its 
mere  presence  cause  an  induced  current,  but  that  a  change  in 
the  relative  positions  of  the  two  circuits,  one  of  which  bears 
a  current,  is  necessary. 

1  This  needle  consists  of  two  needles  of  about  the  same  intensity  with  their  poles 
reversed,  fixed  parallel  with  each  other.  Though  the  needles  nearly  neutralize  each 
other  and  are  therefore  little  affected  by  the  field  of  the  earth's  magnetism,  they  are 
especially  sensitive  to  the  influence  of  the  electric  current  properly  situated. 


548  ETHER    DYNAMICS. 

Experiment  2.  — Place  the  primary  coil  within  the  secondary.  Open 
the  primary  wire  at  some  point  and  then  close  the  circuit  (Fig.  438)  by 
bringing  in  contact  the  extremities  of  the  wires.  A  deflection  is  pro- 
duced. As  soon  as  the  needle  becomes  quiet,  break  the  circuit  by  sepa- 
rating the  wires  ;  a  deflection  in  the  opposite  direction  occurs. 

The  same  phenomena  occur  when  the  primary  current  is 
by  any  means  suddenly  strengthened  or  weakened. 

An  examination  of  the  direction  of  these  currents  enables 
us  to  state  the  facts  as  follows :  Starting  a  current  in  a 
primary,  increasing  the  strength  of  the  primary  current,  or 
moving  the  primary  nearer  while  the  current  is  steady,  pro- 
duces a  transitory  current  in  the  opposite  direction  in  the 
secondary.  Stopping  the  primary,  diminishing  the  strength 
of  the  primary  current,  or  moving  the  primary  away  while 
the  current  is  kept  steady,  causes  a  transitory  current  in  the 
same  direction  in  the  secondary. 

It  is  evident,  therefore,  that  the  conditions  under  which  a 
current  in  the  primary  coil  can  cause  a  current  in  a  neighbor- 
ing secondary  depend  upon  some  change  either  in  the  strength 
of  the  primary  current  or  in  the  relative  positions  of  the 
primary  and  secondary  circuits. 

Experiment  3.  — Introduce  the  bundle,  D  (Fig.  437),  of  soft  iron  wires, 
called  the  core,  into  the  primary  coil,  and  make  and  break  the  primary 
circuit  as  before.  The  deflections  are  now  very  much  increased. 

Experiment  4.  —  Substitute  a  person  for  the  galvanometer  in  the  sec- 
ondary circuit,  the  person  grasping  some  metallic  handles  made  for  the 
purpose  and  used  as  electrodes.  The  person  experiences  at  the  instant 
of  making  and  breaking  a  peculiar  sensation  in  his  wrists  and  arms, 
called  a  shock. 

Experiment  5.  —  Introduce  into  the  primary  circuit  the  automatic 
make-and-break  piece  C  (Fig.  437).  Remove  the  core  from  the  primary 
coil.  Let  a  person  grasp  the  electrodes  of  the  secondary  circuit.  This 
person  experiences  a  series  of  shocks  which  seem  to  him  almost,  if  not 
quite,  continuous.  These  shocks  can  be  intensified  to  suit  the  pleasure 
of  the  person  who  is  receiving  them,  by  gradually  lowering  the  core  into 
the  primary  coil. 


LAW    GOVERNING    E.M.F.    OF    INDUCED    CURRENTS.     549 

Experiment  6.  —  Reflecting  that  you  have  hitherto  found  a  coil  of 
wire  having  a  current  passing  through  it  acting  as  a  magnet,  you  have 
now  an  opportunity  to  try  the 
converse,  i.e.  to  see  whether  a 
magnet  may  not  take  the  place  of 
a  current-bearing  coil.  Introduce 
suddenly  a  bar-magnet  (Fig.  439) 
into  the  secondary  coil,  as  in  Ex- 
periment 1 ;  a  deflection  is  pro- 
daced.  Withdraw  it  and  an  op- 
posite deflection  occurs. 

The  act  by  which  the  prim- 
ary, or  a  magnet,  causes  a  cur- 
rent in  a  neighboring  second- 
ary is   called  magneto-electric  FlG  439 
induction. 

516.  Law  governing  E.M.F.  of  induced  currents. — In  any 
induced  cui*rent  the  E.M.F.  at  any  instant  u  proportional  to 
the  rate  of  change  in  the  number  of  lines  of  force  passing  tit  rough 
the  circuit  at  that  instant.  If  there  be  no  change  in  the 
number  of  lines  there  is  no  induced  E.M.F.,  however  rapid 
the  motion  may  be. 

Experiment  7.  — Introduce  a  long  bar  magnet,  NS  (Fig.  440),  into  a 
short  coil  of  wire,  C,  connected  to  a  galvanometer,  G.  Place  the  coil 

half-way  between    the   poles  of 

^C the  magnet  and  move  it  rapidly 

— )s     (say)  one  centimeter  toward  either 

pole  ;  no  movement  of  the  gal- 
vanometer needle  occurs  although 
all  the  lines  of  force  of  the  mag- 
net pass  through  C. 

Now  place  C  near  one  of  the 
ends  of  the  magnet ;  a  similar  mo- 
no. 440.  tion  produces  a  large  deflection. 

By  means  of  an  induction  coil,  a  current  of  a  few  amperes 
circulating  in  the  primary  under  an  E.M.F.  of  not  more  than 


550 


ETHER    DYNAMICS. 


10  or  20  volts  can  be  caused  to  yield  currents  in  the  secondary 
urged  by  an  E.M.F.  of  many  thousand  volts. 

517.  Faraday's  law  of  induction. — If  any  conducting  cir- 
cuit be  placed  in  the  magnetic  field,  then,  if  a  change  of 
relative  position  or  change  of  strength  of  the  primary  current 
cause  a  change  in  the  number  of  lines  of  force  passing  through 
the  secondary,  an  electro-motive  force  is  set  up  in  the  sec- 
ondary proportional  to  the  rate  at  which  the  number  of  lines 
of  force  included  by  the  secondary  is  varying. 

Consider  the  case  of  induction  by  a  magnet.  Let  S  (Fig. 
441)  be  a  secondary  circuit  and  N  a  magnet  projecting  a  cer- 
tain number  of  lines  of  force 
through  the  circuit.  If  S 
be  moved  nearer  to  the  mag- 
net, say  to  S',  a  much  greater 
number  of  lines  of  force  of 
the  magnet  pass  through  the 
circuit  than  when  in  its  for- 
mer position,  owing  to  the 
divergence  of  the  lines  as 
they  recede  from  the  pole. 

We  may  now  understand, 
in  part,  the  reason  why  a  core  of  soft  iron  so  greatly  increases 
the  induced  current.  It  acts  like  a  lens  in  focusing  or  con- 
centrating more  lines  of  force  from  the  magnetic  inducer 
through  the  aperture  of  the  secondary,  and  therefore  any 
movement  makes  a  greater  rate  of  change,  and  hence  a  greater 
induced  electro-motive  force. 

518.  Earth  induction.  —  Call  to  mind  that  the  earth  itself 
is  a  great  magnet,  and  that  its  lines  of  force  pass  through 
our  atmosphere  from  pole  to  pole,  and  it  will  be  easy  to  con- 
ceive that  the  mere  motion  of  a  coil  of  wire  about  an  axis 
properly  placed *  is  all  that  is  necessary  to  produce  a  current. 


FIG.  441. 


1  The  coil  should  be  placed  at  right  angles  to  the  direction  of  the  dip  at  the 
locality.    Why  ? 


EARTH    INDUCTION. 


551 


Such  a  coil  with  a  galvanometer  G  in  circuit  is  represented 
in  Fig.  442.     The  rotation  of  the  coil  across  the  magnetic 


FIG.  442. 

lines  of  force  of  the  earth  effects  a  change  of  the  number  of 
lines  of  force  passing  through  it,  as  may  be  understood  by 
inspection  of  Fig.  443,  and  this  creates  temporary  currents 
in  the  coil. 

By  examination  of  Fig.  443  it  will  be  seen  that  there  are 
in  each  complete  rotation  of  the  coil  two  points  (as  A  in  the 
figure)  where  the  coil  encloses 
a  maximum  number  of  lines  of 
force.     In  this  position  the  in- 
duced current  vanishes,  for  at 
this    instant    the    number    of 
lines  is  neither  increasing  nor 
diminishing.      As   the    coil  in 
its   rotation   approaches   these     ^  \^ 

points,  the  number  of  lines  of     "^ : 

force  increases,  and  after  leav-  FlG 


552  ETHER    DYNAMICS. 

ing  it  the  number  diminishes.  This  will  evidently  cause  a 
change  in  the  direction  of  the  induced  current  twice  during 
each  revolution.  If  then  by  means  of  a  commutator,  a  (Fig. 
452),  the  direction  of  the  current  in  the  galvanometer  be 
changed  relatively  to  its  direction  in  the  coil  at  each  half- 
revolution,  we  have  an  intermittent  current  constant  in  direc- 
tion through  the  galvanometer. 

519.  Lena's  law.  —  Recurring  to  the  primary  and  secondary 
circuits  we  remark  that  the  motion  of  the  one  or  the  other 
may  be  in  arcs  of  circles  or  in  any  way,  yet  the  motion  may 
always  be  resolved  so  as  to  give  a  resultant  indicating  ap- 
proach or  recession.     The  law  by  which  the  direction  of  the 
induced  current  is  determined  is  known  as  Lenz's  law,  and 
may  be  expressed  as  follows:  "In  all  cases  of  induction  the 
direction  of  the  induced  current  is  such  as  to  oppose  the  motion 
which  produces  it"     Thus  approach  develops  an  opposite  cur- 
rent, since  opposite  currents  resist  approach,  while  recession 
develops  a  current  of  similar  direction,  since  similarly  directed 
currents  attract  one  another  and  thus  resist  recession. 

520.  Mechanical  energy  transformed  into  electric  energy,  and 
vice  versa.  —  It  is,  then,  apparent  that  the  current  developed 
in   the    secondary   circuit  is  at  the  expense  of  mechanical 
energy,   and   thus    mechanical   energy   is    transformed    into 
electric  energy.1 

Keturning  to  the  apparatus  (Figs.  434  and  435)  in  which 
we  have  the  movement  of  a  magnet-pole  in  the  field  of  a 
current,  and  of  a  current  in  the  field  of  a  magnet,  —  if  we 
replace  the  battery  by  a  sensitive  galvanometer,  it  is  evident 
from  the  above  discussion  that  on  rotating  the  magnetic  pole 
(Fig.  444)  or  the  conductor  (Fig.  445),  in  other  words  on 

1  The  student  might  have  been  able  to  prophesy  Lenz's  law  by  reasoning  thus : 
Suppose  coil  B  approaches  circuit  A,  we  know  (1)  that  electrical  energy  appears  in 
B  ;  therefore  from  the  doctrine  of  conservation  of  energy  we  know  (2)  that  work 
must  have  been  done  ;  hence,  if  work  has  been  done,  there  must  have  been  a  repel- 
lent force  between  A  and  B. 


SELF-INDUCTION. 


553 


FIG.  444. 


FIG.  445. 


reversing  the  operations  indicated  in  §  514,  currents  will 
traverse  the  circuits  and  their  presence  may  be  detected  by 
the  deflection  of  the  needles  of  the  galvanometers  G.  If  we 
examine  the  direction  of 
these  induced  currents, 
we  shall  discover  that 
they  are  always  opposite 
to  the  current  which 
would  actually  cause  the 
rotation.  Since  the  in- 
duced current  is  opposite 
in  direction  to  the  cur- 
rent which  would  cause 
the  motion,  it  is  evident 
that  the  electro-magnetic 
effect  of  the  induced  current  is  to  oppose  the  motion  taking 
place  in  the  field,  in  conformity  with  Lenz's  law. 

We  have  seen  that  the  same  apparatus  may  be  used  either 
to  transform  electric  into  mechanical  energy,  or  to  transform 
mechanical  into  electric  energy. 

521.  Self-induction.  —  "Extra  currents"  —  Not  only  does  a 
current  at  starting  and  stopping  or  changing  strength  act  on 
neighboring  conductors,  generating  currents  in  them,  but  it 
acts  upon  itself  by  a  process  which  is  called  self-induction. 
A  current  starting  or  increasing  creates  an  oppositely  directed 
current  not  only  in  its  neighbor,  but  also  in  its  own  wire.  A 
current  does  not  start  instantaneously ;  it  takes  a  certain 
time  —  usually  very  short  —  to  rise  to  its  full  strength.  In 
other  words  the  circular  lines  of  magnetic  force  round  a 
straight  current  do  not  spring  into  existence  instantaneously, 
but  expand  gradually  like  the  widening  ripples  produced 
when  a  stone  is  dropped  into  still  water.  But  when  started 
it  tends  to  persist,  so  that  if  its  circuit  be  suddenly  broken, 
it  does  not  stop  instantaneously.  The  lines  of  force  gradually 


554  ETHER   DYNAMICS. 

collapse,  but  the  point  of  interest  is  that  this  collapse 
gives  rise  to  an  electrical  push,  or  E.M.F.  far  greater  than 
that  which  maintained  the  current,  and  this  sudden  drive 
forward  of  electricity  in  the  wire  at  the  instant  the  circuit  is 
broken  causes  the  spark  seen  on  breaking  a  circuit ;  and  the 
more  sudden  the  break  the  more  violent  the  spark.  If  a 
current  pass  through  the  helix  of  an  electro-magnet,  owing  to 
the  permeability  of  the  iron  a  far  larger  number  of  lines  of 
force  traverse  its  circuit  than  if  the  core  were  removed ;  and 
hence,  at  the  stoppage  of  the  current,  a  correspondingly 
greater  impulse  operates  in  the  wire  and  creates  a  correspond- 
ingly more  powerful  spark.  For  a  similar  reason  the  self- 
induction  is  much  greater  in  a  coil  of  wire  than  if  the  same 
wire  were  laid  out  straight. 

The  self-induction  at  breaking  a  circuit  is  somewhat  analo- 
gous to  the  blow  which  a  high-pressure  service  water-tap 
experiences  when  a  flow  of  water  is  suddenly  arrested  by 
turning  the  tap.  The  water  momentum  often  bursts  the 
pipe.  Similarly  self-induction  often  breaks  through  the  in- 
sulation of  field  magnets  of  dynamos  when  the  current  is 
suddenly  arrested  in  them. 

The  two  effects — the  delay  at  making  circuit,  and  the 
momentum  at  breaking  —  are  frequently  called  "extra  cur- 
rent "  effects,  but  they  are  now  more  commonly  spoken  of  as 
manifestations  of  self-induction  or  quasi-electrical-inertia. 

The  action  of  self  induction  is  to  hinder  the  sudden  rise 
and  fall  of  current  strength  in  a  wire.  Hence,  in  circuits  of 
large  self-induction  it  is  impossible  to  make  very  sudden 
changes  in  the  strength  of  a  current  flowing  through  it. 
This  hinders  telephonic  transmissions  through  long  wires 
and  long  coils,  and  renders  ocean  cable  telegraphing  a  com- 
paratively slow  operation.  It  renders  the  changes  of  cur- 
rents in  the  armatures  of  dynamos  more  sluggish  than  they 
would  otherwise  be. 


INDUCTION    COILS. 


555 


522.  Induction  coils.  —  If  a  core  of  iron,  or,  still  better,  a 
bundle  of  wires  (A  A,  Fig.  446),  be  inserted  in  the  primary 
coil,  it  is  evident  that  it  will  be  magnetized  and  demagnetized 
every  time  the  primary  is  made  and  broken.  The  starting 
and  cessation  of  amperian  currents  in  .the  core  in  the  same 
direction  as  the  primary  current,  and  simultaneously  with  the 
commencement  and  ending  of  the  primary  current,  greatly 


intensifies  the  secondary  current.  To  save  the  trouble  of 
making  and  breaking  by  hand,  as  in  Fig.  438,  the  core  is  also 
utilized  in  the  construction  of  an  automatic  make-and-break 
piece.  A  soft  iron  hammer,  b,  is  connected  with  the  steel 
spring,  c,  which  is  in  turn  connected  with  one  of  the  termi- 
nals of  the  primary  wire.  The  hammer  presses  against  the 
point  of  a  screw,  d,  and  thus,  through  the  screw,  closes  the 
circuit.  But  when  a  current  passes  through  the  primary 
wire,  the  core  becomes  magnetized,  draws  the  hammer  away 
from  the  screw,  and  breaks  the  circuit.  The  circuit  broken, 


556  ETHER    DYNAMICS. 

the  core  loses  its  magnetism,  and  the  hammer  springs  back 
and  closes  the  circuit  again.  Thus  the  spring  and  hammer 
vibrate,  and  open  and  close  the  primary  circuit  with  great 
rapidity.  An  instrument  made  on  these  principles  is  called 
an  induction  coil. 

523.  Ruhmkorff's  coil.  —  This  instrument  has  the  impor- 
tant addition  to  the  parts  already  explained  of  a  condenser, 
B  B.  This  consists  of  two  sets  of  layers  of  tinfoil  separated 
by  paraffined  paper  ;  the  layers  are  connected  alternately  with 
one  and  the  other  electrode  of  the  battery,  as  the  figure  shows, 
so  that  they  serve  as  a  sort  of  expansion  of  the  primary  wire. 
When  the  circuit  is  broken,  the  extra  current  tends  to  jump 
across  at  b,  and  to  vaporize  the  points  of  contact,  and  form 
a  bridge  with  the  vapor  of  metal  that  would  prolong  the 
time  of  breaking.  But,  when  the  condenser  is  attached,  the 
extra  current  finds  an  escape  into  it  easier  than  to  jump 
across  at  b,  so  the  vaporizing  of  the  contact  is  avoided,  and 
the  time  of  breaking  being  much  shortened,  the  secondary  is 
much  more  intense. 

The  primary  helices  of  induction  coils  consist  of  compara- 
tively few  turns  of  coarse  insulated  wire  ;  but  the  secondary 
helices  contain  many  turns  of  very  fine  wire,  insulated  with 
great  care.  The  secondary  current  is,  at  breaking,  as  we 
ought  to  expect  from  the  extreme  rapidity  with  which  the 
primary  circuit  is  broken,  distinguished  from  the  primary,  or 
galvanic  current,  by  its  vastly  greater  E.M.F.,  or  power  to 
overcome  resistances.  A  coil  constructed  for  Mr.  Spottis- 
woode  of  London  has  two  hundred  and  eighty  miles  of  wire 
in  its  secondary  coil.  With  five  Grove  cells  this  coil  gives  a 
secondary  spark  forty-two  inches  long,  and  perforates  glass 
three  inches  thick.  Many  brilliant  experiments  may  be  per- 
formed with  these  coils. 

Experiment  8.  —  Connect  a  battery  of  two  Bunsen  cells,  in  multiple 
arc,  with  a  Kuhmkorff  coil  (Fig.  447).  Bring  the  electrodes  of  the  sec- 


DYNAMO    DEFINED.  557 

ondary  coil  within  from  one-fourth  of  an  inch  to  one  inch  of  each  other, 
according  to  the  capacity  of  the 
instrument.      A  series  of  sparks 
in  rapid  succession  pass  from  pole 
to  pole. 

Experiment  9.  —  Introduce  a 
Geissler  tube,  A,  into  the  secon- 
dary circuit.  These  tubes  con- 
tain highly  rarefied  gases  of  dif- 
ferent kinds.  Platinum  wires  are 
sealed  into  the  glass  at  each  end 
to  conduct  the  electric  current 
through  the  glass.  The  sparks 
become  diffused  in  these  tubes  so  FlG 

as  to  illuminate  the  entire  tubes 

with  an  almost  continuous  glow.  Observe  that  the  electrodes  are  sepa- 
rated from  each  other  much  more  widely  than  would  be  admissible  in 
air  of  ordinary  density,  showing  that  rarefied  gases  offer  less  resistance 
than  dense  gases.  Gases  have  been  so  highly  rarefied,  however,  that  an 
electric  current  would  not  pass. 


SECTION   XIX. 

DYNAMO-ELECTRIC    MACHINES. 

524.  Dynamo   defined.  —  The   greatest    single   advance   in 
industrial  life  made  during  the  present  century  is  the  inven- 
tion and  perfection  of  the  Dynamo- Electric  Machine. 

The  dynamo  is  a  device  for  changing  mechanical  energy 
into  electric  energy.  In  the  most  improved  types  of  dynamos 
this  is  done  with  a  loss  of  less  than  5  per  cent  of  the  energy. 

525.  Principle  of  the  dynamo.1  —  The  illustrations  of  elec- 
tro-magnetic induction  given  in  the  preceding  section  suggest 

1  Faraday's  theory  is  this  :  Moving  a  wire  across  a  space  in  which  there  are  mag- 
netic lines,  so  as  to  cut  across  those  lines,  sets  up  magnetic  whirls  around  the  mov- 
ing wire,  or,  in  other  words,  generates  a  so-called  current  of  electricity  in  that  wire. 
It  is  necessary,  however,  that  the  moving  conductor  should  so  cut  the  lines  of  force 
as  to  alter  the  number  of  lines  of  force  that  pass  through  the  circuit  of  which  the 
moving  conductor  forms  a  part. 


558 


ETHER    DYNAMICS. 


the  explanation  of  the  action  of  a  dynamo.  The  action  of  the 
dynamo  machine  depends  upon  the  principle  that  when  lines 
of  magnetic  force  are  cut  by  a  wire  a  difference  of  potential 
is  produced  in  the  wire,  and  hence  a  current  flows  through 
the  wire,  if  its  ends  be  connected  so  as  to  form  a  closed  cir- 
cuit. This  was  illustrated  in  connection  with  Fig.  441,  and 
is  illustrated  by  the  following  experiment. 

Experiment  1.  —  Connect  a  flat  coil  of  about  two  inches  in  diameter, 
having  several  turns  of  wire,  with  a  delicate  galvanometer,  and  rotate 
the  coil  at  one  of  the  poles  of  a  strong  magnet  on  an  axis  at  right  angles 
to  the  axis  of  the  magnet  and  the  lines  of  force,  as  illustrated  in  Fig.  448. 

The  horizontal  arrow  a  indicates  the  direction  of  the  mag- 
netic lines  of  force,  the  horizontal  arrow  b  the  direction  of 
motion  of  the  end  of  the  coil  of  wire,  and  the  vertical  arrow 


FIG.  448. 

c  the  direction  of  the  current  induced  in  the  coil  of  wire  from 
the  movement  of  the  coil  across  the  field  of  magnetic  force  in 
such  a  manner  as  to  cut  lines  of  force. 

If  the  coil  be  moved  rapidly  in  front  of  the  magnet,  the 
current  is  stronger  and  hence  the  E.M.F.  must  be  greater 
than  if  it  be  moved  slowly. 

Also  if  the  number  of  turns  of  wire  be  increased  the 
E.M.F.  is  correspondingly  increased,  as  will  be  shown  by  the 
increased  strength  of  current.  The  increase  in  strength  of 
current  will  not  be  so  great  as  the  increase  of  the  E.M.F. 


PRINCIPLE    OF   THE   DYNAMO.  559 

unless  the  galvanometer  resistance  is  very  large  as  compared 
with  that  of  the  coil. 

Every  portion  of  the  wire  that  cuts  lines  of  force  must, 
then,  evidently  develop  E.M.F.,  and  the  total  E.M.F.  is  the 
sum  of  all  that  is  induced  in  different  parts  of  the  coil. 

If  the  strength  of  the  magnet  be  increased  the  number  of 
lines  of  force,  and  consequently  the  strength  of  current,  will 
be  increased.  Again,  if  the  coil  be  of  high  resistance,  the 
current  will  be  feeble ;  if  of  low,  the  current  is  stronger. 

We  may  continue  our  experiment  still  further  by  inserting 
a  bar  or  disk  of  soft  iron  into  the  coil  and  again  moving  the 
end  of  the  coil  through  the  field  of  force  in  front  of  the  north 
pole  of  the  magnet.  A  very  decided  increase  in  the  strength 
of  current  is  observed.  If,  further,  another  bar  magnet  be 
placed  so  that  its  south  end  faces  the  other  end  of  the  coil, 
and  the  coil  be  fixed  at  its  center  while  its  two  ends  are 
made  to  rotate  past  the  two  poles,  more  lines  of  force  are  cut 
and  greater  E.M.F.  is  developed,  as  is  seen  from  the  increased 
strength  of  current. 

The  same  effect  can  be  obtained  by  using  a  single  magnet 
of  horse-shoe  form,  and  placing  the  coil  between  its  two 
opposite  poles. 

We  have  now  found  that  the  strength  of  current  and 
E.M.F.  depend  upon  (1)  the  rapidity  of  motion  of  the  wire 
through  the  field;  (2)  the  number  of  turns  of  the  wire  ;  and 
(3)  the  number  of  lines  of  force  cut,  or  the  strength  of  field. 

A  powerful  electro-magnet  is  preferable  as  an  inducer  to  a 
permanent  magnet,  as  its  strength  or  magnetic  density  can  be 
made  much  greater. 

526.  Relation  existing  between  the  direction  of  the  lines  of 
force,  the  motion  of  the  coil,  and  the  direction  of  the  current.  — 
This  relation  may  be  conveniently  remembered  by  placing 
the  thumb,  forefinger,  and  middle  finger  of  the  right  hand  all 
at  right  angles  to  one  another,  as  in  Fig.  449,  and  imagining 


560 


ETHER    DYNAMICS. 


the  forefinger  to  indicate  the  direction  of  the  magnetic  lines 
of  force   (FORe,  FOlice),  the  thumb  that  of  the  motion  of 

the  conducting  wire 
(thuMb,  Motion),  and 
the  middle  finger  that 
of  the  direction  of  the 
induced  current  (mid- 
dle. Induced).  If  the 
hand,  with  the  fingers 
in  this  relative  po- 
sition, be  held  so  that 
the  direction  of  the 


FIG.  449. 


forefinger      coincides 


with  the  direction  of 

the  lines  of  force  (as  indicated  by  a  test  needle),  and  the 
thumb  points  in  the  direction  of  motion  of  the  part  of  the 
conductor  under  consideration,  the  middle  finger  will  indi- 
cate the  direction  of  the  induced  current. 

527.  The  dynamo.  —  We  are  now  prepared  to  study  the 
action  of  the  dynamo.  Our  magnet,  which  is  commonly  an 
electro- magnet,  is  called  the 
field  magnet,  and  our  coil  or 
series  of  coils  of  wire,  which 
is  generally  made  to  move  in 
front  of  the  poles  of  the  field 
magnet,  is  called  the  armature. 
The  armature  is  that  part  of 
the  electric  circuit  in  which 
the  induced  current  is  gene- 
rated. Like  the  battery,  it 
may  be  considered  as  the 
source  of  the  current.  The  number  of  lines  of  force  passing 
through  a  circuit  may  in  general  be  changed  in  two  ways  : 
either  (1)  by  moving  the  circuit  through  a  field  in  which  the 


—  ^^  L 

I 

A 

fe-  1 

\ 

,, 

FIG.  450. 


THE    DYNAMO. 


561 


density  of  the  lines  of  force  varies,  as  represented  in  Fig. 
450;  or  (2)  by  rotating  the  plane  of  the  circuit  so  as  to  change 
the  angle  which  it  makes  with  the  line  of  force,  thus  increasing 
or  decreasing  the  number  which  the  circuit  encloses  (Fig.  443). 
The  former  of  these  methods  is  adopted  in  the  Thomson -Houston 
and  the  Westinghouse  alternate-current  dynamos ;  the  latter 
method  is  employed  in  the  Edison  and  the  Weston  systems. 
A  common  simple 
form  of  dynamo  is 
illustrated  in  Fig. 
451.  A  large  mass 
or  bar  of  soft  iron 
of  the  U  form,  sur- 
rounded with  a  coil 
of  insulated  wire, 
and  terminating  in 
the  pole  pieces  N. 
and  S.,  forms  the 
field  magnet.  The 
armature  consists 

of  a  single  rectangular  loop  of  wire,  which  is  fixed  to  a  hori- 
zontal axis,  and  terminates  in  two  rings  of  metal,  a  and  b, 
which  are  fixed  to  the  axle,  but  insulated  from  it. 

When  a  current  passes  through  the  field  coils,  and  the  core 
becomes  magnetized,  lines  of  force  will  cross  and  fill  the  space 
between  the  pole  pieces  of  the  field  magnet.  As  these  lines 
are  cut  by  the  horizontal  parts  of  the  rotating  wire,  an  E.'M.F. 
is  generated  in  these  parts,  and  a  current  flows  in  the  direc- 
tion indicated  by  the  arrows. 

Apply  the  preceding  rule  for  determining  the  direction  of 
the  current  by  letting  the  forefinger  of  the  right  hand  take 
the  direction  of  the  magnetic  lines  of  force,  the  thumb  the 
direction  of  motion  at  right  angles  to  the  lines  of  force,  and 
the  middle  finger  the  direction  of  the  induced  current.  The 


FIG.  451. 


562 


ETHER    DYNAMICS. 


end  portions  of  the  loop  do  not  cut  lines  of  force,  and  there- 
fore no  E.M.F.  is  generated  in  them,  and  they  are  dead  wire, 
—  simply  serving  as  conductors  to  complete  the  circuit.  A 
metallic  or  carbon  brush,  m,  touches  and  carries  off  the  cur- 
rent from  the  lower  horizontal  segment  of  the  rectangular 
coil.  This  current  flows  through  the  external  resistance,  R, 
and  completes  the  circuit  through  the  brush,  n,  to  the  ring,  &, 
and  the  upper  half  of  the  loop.  The  current  will  continue  to 
flow  in  this  direction  while  the  loop  moves  through  one  half 
of  a  revolution.  Since  the  lines  of  force  are  cut  in  the  oppo- 
site direction  in  the  next  half  revolution,  the  current  will  be 
reversed  in  the  armature  wire  and  also  through  the  external 
circuit.  Thus  with  each  half  revolution  of  the  armature  a 
reversal  of  the  current  takes  place.  This,  then,  would  be 
called  an  alternating  current  dynamo. 

528.  The  commutator.  —  The  alternating  current  is  not 
adapted  to  all  uses,  and  for  many  purposes  it  is  desirable  to 
have  the  current  continuously  flowing  in  the  same  direction. 
To  accomplish  this  a  commutator  is  attached  to  the  axis  of 
the  armature. 

In  Fig.  452  the  two  brass  rings  a  and  b  are  replaced  by  a 
single  brass  tube  divided  into  two  parts  by  cutting  it  length- 
wise. These  two  segments  are  attached  to  but  insulated 

from   the   axis,   and   are 

jf     ^     connected  with  the  sepa- 

rate ends  of  the  armature 
wire.  When  the  plane 
of  the  armature  coil  is 
perpendicular  to  the  line 
of  force  passing  from  N 
to  S,  as  in  Fig.  452,  no 
lines  of  force  are  being 
cut,  and  hence  no  E.M.F.  is  developed  and  no  current  flows 
through  the  loop.  But  the  instant  it  moves  out  of  the  perpen- 


THE    COMMUTATOR.  563 

dicular  in  the  direction  of  the  arrow,  lines  of  force  will  be 
cut,  and  as  the  lower  segment  of  the  loop  is  moving  upward 
past  the  pole  S,  and  the  other  segment  is  moving  downward 
in  front  of  the  pole  N",  a  positive  current  flows  from  the  loop 
through  the  segment  a,  the  brush  m,  the  resistance  R,  the 
brush  n,  and  the  strip  of  the  commutator  b.  During  the  next 
half  of  a  revolution  the  lines  of  force  will  be  cut  from  an 
opposite  direction  by  each  of  the  horizontal  segments  of  the 
armature  loop,  and  hence  the  current  will  be  reversed.  But 
the  segment  b  of  the  commutator  will  now  be  in  contact  with 
the  brush  m ;  and  although  the  current  is  reversed  in  the 
armature  it  will  flow  off  at  the  'brush  m  as  before.  Inasmuch 
as  no  E.M.F.  is  developed  when  the  plane  of  the  loop  is  per- 
pendicular to  the  lines  of  force,  it  is  at  this  point  that  the 
brushes  pass  from  one  segment  to  the  other.  If  the  segments 
were  to  leave  the  brushes  while  the  coil  was  cutting  lines  of 
force,  it  is  evident  that  a  spark  would  be  formed  if  the  coil 
were  revolving  with  great  velocity.  The  maximum  spark 
would  be  given  off  if  the  segments  left  the  brushes  when  the 
loop  is  parallel  to  the  lines  of  force. 

Thus  by  means  of  the  commutators  and  brushes,  reversal 
of  the  current  is  prevented  in  the  external  circuit,  although 
the  current  in  the  armature  reverses  with  each  half  revolu- 
tion. This  arrangement  would  constitute  a  direct-current 
dynamo.  We  may  have  two  turns  of  wire  before  connecting 
with  the  commutator  strips,  giving  twice  the  E.M.F.,  or  three 
turns,  giving  three  times  the  E.M.F. ;  i.e.  the  E.M.F.  will  be 
proportional  to  the  number  of  turns  of  wire  in  the  coil. 
Again,  instead  of  having  only  one  coil  we  may  have  two  or 
any  number  of  coils,  each  separate  from  the  others,  and  ter- 
minating in  strips  or  segments  which  are  on  opposite  sides 
of  the  commutator.  Generally  the  coils  are  connected  in 
series,  thus  making  any  segment  a  terminal  of  one  coil  and 
the  beginning  of  the  next. 


564  ETHER    DYNAMICS. 

529.  Eddy  currents. 

In  Experiment  1  it  was  observed  that  with  a  mass  of  iron  within 
our  coil  a  greater  current  was  produced  when  the  coil  was  moved 
through  the  magnetic  field.  So,  as  in  Fig.  461,  the  coils  of  wire 
may  be  wound  around  a  cylinder  or  drum  of  iron,  winding  along 
the  length  of  the  drum  and  over  the  ends.  From  what  we  have 
previously  seen  it  was  evident  that  differences  of  potential  will  be 
set  up  in  the  iron,  and,  as  it  is  a  good  conductor,  currents  will  flow 
through  the  iron  unless  prevented,  and  heat  it.  These  eddy  currents 
(commonly  called  "Foucault  currents")  are  prevented  by  making 
the  armature  core  laminated,  i.e.  having  it  made  up  of  iron  discs  or 
plates  insulated  from  one  another.1 

530.  The  Gramme  armature.  —  The  machine  we  have  de- 
scribed has  the  drum  or  Siemens  armature,  and  is  now  more 
commonly  used.     Another  form  of  machine  frequently  em- 
ployed has  the  ring  or  Gramme  armature.     In  this  form  of 


FIG.  453. 

armature  the  core  consists  of  an  iron  ring  or  hollow  cylinder 
instead  of  a  closed  cylinder  or  drum,  and  the  wire  is  wound 

1  It  must  be  noticed  that  the  armature  current,  because  of  its  action  on  the  core 
tends  to  distort  the  magnetic  field  in  the  direction  of  the  rotation.  This  distortion 
necessitates  a  change  of  position  or  lead  of  the  brushes  on  the  commutator,  in  the 
direction  of  the  rotation  of  the  motion  of  the  armature. 


THE    GRAMME    ARMATURE. 


565 


round  this  ring  instead  of  over  it.  The  ring  may  be  com- 
posed of  a  bundle  of  soft  iron  wires,  as  shown  in  Fig.  453 
(where  a  portion  of  the  ring  is  cut  away),  surrounded  by 
sectional  coils  of  what  is  virtually  an  endless  wire.  A  wire 
from  each  section  is  carried  to  and  connected  electrically  with 
a  section  of  the  commutator. 

Fig.  454  is  a  skeleton  diagram  of  a  generator  of  this  kind  ; 
and  Fig.  455  is  a  portion  of  the  same,  showing  lines  of  force 
traversing  the  field  pieces  and  the  armature.  The  lines  are 


FlG.  454. 

supposed  not  to  be  distorted  by  the  motion  of  the  armature. 
When  the  coils  with  the  segments  are  connected  in  series 
it  is  evident  that  those  coils  moving  downward  in  front  of 
the  pole  piece  N  (Fig.  454)  develop  E.M.F.  urging  the  cur- 
rent away  from  the  brush  n  and  towards  the  brush  m.  At 
the  same  time  those  coils  moving  upward  in  front  of  the 
pole-piece  S  also  have  currents  urged  towards  the  brush  m. 
Thus  the  armature  is  virtually  divided  into  two  equal  parts, 
each  half  having  currents  flowing  to  the  brush  m.  The 
brushes  must  therefore  be  placed  on  opposite  sides  of  the 
commutator  in  such  a  position  that  a  line  connecting  them 


566 


ETHER    DYNAMICS. 


will  be  perpendicular  to  the  lines  of  force.     They  will  then 
lead   the   current   from   the   armature   where   the   potential 


FIG.  455. 

difference  is  a  maximum  and  from  the  coils  that  are  in  the 
field  of  least  action. 

531.  Classes  of  dynamos1.  — Dynamos  may  be  divided  into 
different  classes  according  to  the  method  by  which  their 
field  magnets  are  excited.  Fig.  456  illustrates  a  magneto- 
electric  machine,  where  the  field  magnet  is  a  permanent  steel 
magnet.  This  form  of  machine  is  seldom  used,  since  a  per- 
manent steel  magnet  cannot  be  made  as  powerful  as  an 
electro-magnet  having  a  soft  iron  core  of  equal  mass. 

Fig.  451  illustrates  a  separately  excited  dynamo,  where  the 
field  magnet  coils  receive  their  currents  from  a  separate 
generator,  e.g.  a  battery,  and  not  from  the  armature  coils. 

1  For  the  characteristics  of  the  various  classes  of  dynamos,  as  well  as  for  a  most 
lucid  and  comprehensive  treatment  of  dynamos  generally,  see  Dynamo-Electric 
Machinery,  by  S.  P.  Thompson. 


CLASSES    OF    DYNAMOS. 


567 


Since  an  alternating  current  dynamo  does  not  produce  a  con- 
stant magnetic  field,  alternating  dynamos,   in  general,  are 
separately  excited.     Such  are  the  West- 
inghouse  and  the  Thomson-Houston  incan-     /  ^\ 

descent-lighting  dynamos. 

Fig.  454  is  a  series  dynamo,  where  the 
coils  of  the  field  magnet  are  joined  in 
series  with  the  armature  so  that  the  en- 
tire current  passes  through  these  coils. 

Fig.  457  illustrates  a  shunt  machine, 
where  the  field-coil  serves  as  a  shunt  to 
the  external  circuit.  L  is  the  main  wire 
and  I  is  the  shunt  wire.  In  the  shunt 

machine 
only  a  part 

of  the  current  generated  in 
the  armature  passes  through 
the  field-coils. 

A   dynamo   is    said   to   be 
"  self -exciting  "      when     the 
whole  (Fig.  454)  or  any  part 
(Fig.  457)  of  the  current  which 
is  produced  is  used  to  magnet- 
ize the  field  magnets.    Such 
are  the  Edison  incandescent 
dynamos. 

The  fields,  after  being 
once  excited  from  any 
source,  e.g.  another  dynamo, 
always  retain  a  little  re- 
sidual magnetism,  so  that 
when  the  armature  begins 
to  rotate,  a  slight  current 
FIG.  457.  is  at  once  induced  in  it. 


568 


ETHER    DYNAMICS. 


This  strengthens  the  field,  and  the  stronger  field  reacts  to 
increase  the  current,  so  that  the  current  soon  rises  to  its 
normal  strength. 

More  than  one  set  of  coils  may  be  used  on  the  field  mag- 
nets, and  these  coils  may  receive  currents  from  different 
sources.  Dynamos  employing  these  are  called  compound 
wound  machines.  They  may  be  arranged  for  constant  poten- 
tial, or  constant  current.  A  combination  of  the  series  and 
separately  excited,  or  of  series  and  shunt,  gives  constant 
potential ;  while  a  combination  of  shunt  and  separately  ex- 
cited gives  constant  current. 

All  figures  hitherto  have  been  diagrammatic  representations 
of  dynamos.  Fig.  458  represents  a  modern  typical  dynamo, 


W 


FK;.  458. 


the  Weston.  Large  field  magnets,  A  and  B,  are  placed  each 
side  of  the  revolving  armature.  A  steam-engine  communi- 
cates motion  to  the  armature  by  means  of  a  belt  passing  over 
the  circumference  of  the  wheel  W.  The  pole-pieces,  as  will 


CLASSES    OF    DYNAMOS. 


569 


be  seen  in  the  cut,  are  laminated  to  prevent  eddy-currents, 
and  the  magnets  are  shunt-wound. 

Fig.  459  represents  one  of  the  most  common  forms  of  the 
Edison  dynamo,  and  Fig.  460  is  a  skeleton  diagram  correspond- 


FlG.  459. 


ing  in  most  particulars  with  the  first.  It  will  be  seen  by  the 
latter  figure  that  it  is  a  shunt-wound  dynamo.  The  terminals 
of  an  automatic  regulator  for  regulating  the  intensity  of  the 
current  are  inserted  in  the  binding  screws  a  a.  P  is  a  so-called 
pilot-lamp  joined  in  multiple  arc  to  the  field-coils.  F  F  are 
leading  wires  ;  and  b  b  are  points  for  the  attachment  of  fuses. 
These  fuses  are  to  the  dynamo  what  the  safety-valve  is  to  the 


570 


ETHER   DYNAMICS. 


steam  boiler ;  they  protect  the  dynamo  from  injury  by  over- 
pressure, since  an  overload  is  sure  to  cause  them  to  melt  and 
thus  interrupt  the  current. 

532.  Classes  of  armatures?  —  (1)  In  ring-armatures  the 
coils  are  wound  round  a  ring-shaped  core,  as  shown  in  Fig. 
454.  Example  :  the  Gramme  and  the  Brush. 

(2)  In  drum-armatures  the  coils  are  wound  longitudinally 


FIG.  460. 


FIG.  461. 


over  a  cylinder  or  drum,  as  in  Fig.  461.  Examples  :  the 
Edison,  the  Weston,  and  the  Siemens. 

(3)  In  pole  or  radial  armatures  the  coils  are  wound  on  sep- 
arate poles  that  project  radially  from  a  cylinder  (Fig.  462). 

In  alternating  current  dynamos,  in  order  to  obtain  the  rapid 
reversals  (in  some  machines  as  many  as  200  per  second)  of 
currents  in  opposition  to  resistance  offered  by  self-induction, 
a  number  of  poles  of  alternate  polarity  are  employed. 

The  separate  coils  may  be  coupled  either  in  series  or  in 
multiple-arc.  When  low  E.M.F.  is  desired,  as  for  incan- 
descent lamps  in  multiple  arc,  the  separate  coils  are  united 


1  The  Thomson-Houston  armature  cannot  be  classified,  as  it  is  unique  among 
armatures.     It  is  spheroidal  in  shape. 


REVERSIBILITY    OF    THE    DYNAMO. 


571 


in  multiple  arc  ;   but  where  great  E.M.F.  is  required,  they 
are  connected  in  series,  as  shown  in  Figs.  462  and  463. 


FIG.  463. 

(4)  Disk-armatures  are  usually  composed  of  a  number  of 
separate  coils  set  side  by  side  in  the  circumference  of  a  disk 
(Fig.  463).  Mechanical  difficulties  in  their  construction  have 
not  permitted  them  as  yet  to  compete  successfully  with  the 
first  two  types  named  above. 


SECTION   XX. 

ELECTRIC    MOTOR. 

533.  Reversibility  of  the  dynamo.  —  This  subject  has  al- 
ready been  touched  upon  in  §§  512  and  520  ;  it  only  remains 
to  treat  it  a  little  more  in  detail.  If  a  current  from  an 
external  source,  e.g.  a  battery  or  another  dynamo,  be  passed 
through  the  armature  and  field  magnet  of  a  direct-current 
dynamo,  it  will  excite  the  armature  and  make  of  it  an  electro- 
magnet and  will  also  excite  the  fields.  The  current  will  enter 
at  the  terminals  and  will  pass  through  the  commutator  into 
the  armature.  The  relation  of  parts  is  such  that  in  doing 
this  it  will  develop  N  and  S  poles  in  parts  of  the  periphery 
of  the  armature  distant  from  the  N  and  S  poles  of  the  fields. 
Hence  a  stress  will  be  set  up  between  the  armature  and  the 
poles  of  the  field  magnet  tending  to  move  the  former  a  little 


572  ETHEK    DYNAMICS. 

in  the  opposite  direction  to  that  in  which  it  is  compelled  to 
move  when  generating  a  current.  Bnt  a-s  soon  as  it  has 
turned  a  short  distance,  the  action  of  the  commutator  shifts 
the  current,  and  new  poles  are  established  in  the  armature 
back  of  the  first  and  in  the  same  relative  positions  which  they 
at  first  occupied.  The  armature  continues  to  rotate  as  the 
new  poles  are  attracted  and  repelled,  and  the  action  goes  on 
so  long  as  a  current  is  supplied.  Obviously  if  there  were  no 
commutator  the  poles  of  the  armature  would  be  fixed,  and  it 
never  could  rotate  through  a  greater  angle  than  180°. 

It  is  evident,  then,  that  if  two  dynamos  be  connected  by 
wires  in  the  same  circuit  and  if  the  armature  of  one  be 
rotated,  the  armature  of  the  other  will  rotate  in  a  reverse 
direction  as  soon  «as  "the  current  transmitted  from  the  first 
attains  a  certain  intensity. 

If  in  a  separately-excited  direct-current  dynamo,  or  in  a 
magneto-dynamo  (Fig.  456),  or  in  a  series  dynamo  (Fig.  454), 
we  substitute  a  dynamo  or  other  current  generator  for  the 
resistance  E,  and  the  current  be  made  to  flow  through  the 
armature  in  the  same  direction  as  when  generating  a  current 
as  shown  by  the  arrows,  the  armature  will  tend  to  rotate  in 
the  opposite  direction  from  that  indicated  by  the  barbed  ar- 
rows. If  the  current  from  our  generator  flows  in  the  opposite 
direction  from  that  shown  by  the  arrows,  the  armature 
will  rotate  in  the  same  direction  as  the  barbed  arrow.  If 
again  we  use  a  shunt  dynamo  (Fig.  457),  placing  a  generator 
in  the  main  circuit  L  with  a  current  flowing  into  the  armature 
in  the  direction  of  the  arrow,  the  current  will  divide  at  the 
negative  brush,  a  part  going  through  the  field-magnet  coils, 
but  in  a  direction  opposite  to  that  in  which  it  flows  when  the 
dynamo  is  used  as  a  generator.  Hence  the  polarity  of  the 
field-magnet  is  reversed,  and  the  armature  will  rotate  in  the 
same  direction  when  receiving  a  current  as  when  generating 
a  similar  current. 


THE   ACTION    OF   THE   DYNAMO-MOTOK.  573 

It  is  now  evident  that  the  dynamo  is  a  reversible  machine, 
in  which  mechanical  energy  can  be  changed  directly  into 
electrical  energy  or  electrical  energy  into  mechanical  energy. 
When  the  dynamo  is  used  for  the  latter  transformation,  it  is 
commonly  known  as  an  electric  motor.  In  other  words  a 
modern  motor  is  a  dynamo  reversed.  The  discovery  of  the 
reversibility  of  the  dynamo  is  considered  to  be  one  of  high 
importance.  The  reversibility  leads  to  some  curious  results. 
For  example,  when  a  car  on  an  electric  railway  is  descending 
a  hill,  its  motor,  instead  of  driving  the  car,  might  be  driven 
by  it  and  thereby  become  a  dynamo  and  send  a  current  into 
the  line  to  drive  or  help  drive  other  cars  in  the  same  circuit. 
It  would  be  possible  for  one  car  of  an  electric  system,  in 
running  down  a  steep  hill,  to  have  its  mechanical  energy 
absorbed  by  its  motor  acting  as  a  dynamo  (and  thus  serving 
as  a  brake  to  retard  its  motion),  and  thus  to  draw  another  car 
of  the  same  system  up  a  hill  miles  distant. 

534.  The  action  of  the  dynamo-motor.  —  This  may  be  under- 
stood by  referring  to  Fig.  464,  and  imagining  a  generator 
to  replace  the  external  resistance  R.  Suppose  the  current 
from  the  generator  enters 
at  the  brushes  and  flows 
in  the  loop  in  the  direc- 
tion of  the  arrows  ;  then 
the  upper  face  of  the  loop 
will  have  S  polarity  and 
the  under  face  N  polarity. 
Then  by  the  mutual  action 
between  this  field  and 
that  of  the  magnet  N  S,  a  rotation  of  the  loop  will  take  place 
clockwise  till  it  comes  into  a  vertical  position.  When  it 
reaches  this  position,  however,  the  brushes  are  so  arranged 
with  reference  to  the  commutator  segments  that  the  current 
in  the  loop  —  and  hence  its  polarity  —  is  reversed.  Even  if 


574 


ETHER    DYNAMICS. 


there  were  only  one  loop  its  inertia  would  be  sufficient  to 
carry  it  by  this  critical  position,  and  the  loop  would  continue 
to  rotate  in  the  attempt  again  to  bring  its  field  parallel  to  that 
of  N  S  ;  but  as  a  matter  of  fact  the  other  loops  in  the 
armature  are  never  in  the  critical  position  at  the  same  time 
as  the  one  considered,  and  those  on  each  side  of  it  conspire 
to  produce  a  continuous  rotation  in  the  same  direction. 

If  the  armature  contain  a  soft  iron  core,  as  is  usually  the 
case,  the  intensity  of  the  field  will  be  much  greater  and  the 
mechanical  effect  correspondingly  increased. 

Fig.  465  represents  a  modern  form  of  motor  weighing  only 
two  or  three  pounds,  and  capable,  when  worked  with  four  or 

five  Bunsen  cells,  of 
operating  a  sewing- 
machine  or  running  a 
small  saw.  It  consists 
of  a  movable  coil  with- 
in a  fixed  coil.  The 
wires  of  each  coil  are 
wound  on  an  iron 
frame-work,  the  two 
opposite  edges  of  the 
iron  being  north  and  south  poles  when  the  current  is  passing. 
The  inner  coil  is  furnished  with  a  commutator,  which 
reverses  the  current  as 
soon  as  opposite  poles 
of  the  inner  and  outer 
coils  are  opposed.  A 
represents  the  outer 
coil  of  wires,  B  one 
pole  of  the  fixed  electro- 
magnet made  by  it,  and  C  the  commutator  by  which  the  inner 
coil  has  the  current  reversed  each  half  revolution.  Fig.  466 
shows  the  inner  coil  (D),  whose  terminals  are  attached  to  the 


FIG.  465. 


FIG.  466. 


THE   INDUCTION   COIL   REVERSIBLE. 


575 


two  halves  of  the  spindle  (E),  which  are  carefully  insulated 

from  each  other.     In  Fig.  467  the  commutator  is  shown  in 

plan.    The  current  enters  the  inner  coil  through  the  spring  H, 

which  carries  a  friction  roller  (L 

working  on  the  commutator  E; 

after  traversing  the  coil  it  re- 

turns  to  the  upper  half  of  E, 

and  thence  passes  by  the  spring 

G  to  K,  from  K  through  the 

outer   coil  to  L,  and  from   L 

back  to  the  battery.  FlG-  4°7. 

The  dynamo  as  a  generator  and  the  dynamo  as  a  motor 
have  already  revolutionized  electrical  economics  and  relegated 
the  battery  to  an  honored  position  among  things  of  the  past. 
The  electric  motor  is  now  extensively  used  in  large  towns 
and  cities,  in  factories  where  power  is  not  continuously 
needed.  Its  widest  application  at  present  is  in  the  propul- 
sion of  street  cars.  The  current  is  generated  by  dynamos  at 
some  central  power  house  and  thence  distributed  to  the 
motors  at  various  points  on  the  circuit. 


SECTION   XXI. 

THE    TRANSFORMER. 

535.  The  induction  coil  reversible.  —  An  induction  coil  is 
in  a  certain  sense  a  reversible  machine.  If  a  current  of 
considerable  strength  circulate  under  small  E.M.F.  in  the 
primary,  then  variations  in  its  strength  give  rise  to  very 
weak  currents  of  exceedingly  high  E.M.F.  in  the  secondary. 
Conversely,  if  we  cause  to  circulate  in  the  secondary  weak 
currents  under  very  high  E.M.F.,  by  their  fluctuations  there 
will  be  generated  in  the  primary  strong  currents  of  small 
E.M.F.  We  do  not  in  either  case  create  electric  energy. 


576  ETHER    DYNAMICS. 

Electric  activity  (or  power)  is  the  product  of  two  factors, 
current  and  electro-motive  force.  The  induction  coil  enables 
us  to  increase  one  of  these  factors  at  the  expense  of  the 
other,  and  to  transform  electric  energy  in  form  much  as  a 
mechanical  power  (e.g.  a  lever)  enables  us  to  convert  a  quan- 
tity of  work  which  consists  of  small  stress  exerted  through 
a  great  distance  into  a  large  stress  exerted  through  a  small 
distance. 

The  transformer  —  sometimes  called  a  converter — is  merely 
an  induction  coil  used  to  change  the  relation  of  the  number 
of  volts  to  the  number  of  amperes  of  any  current.  In  a 
perfect  transformer  the  number  of  watts  in  the  primary 
equals  the  number  of  watts  in  the  secondary. 

The  Ruhmkorff  coil  as  ordinarily  used  may  be  regarded  as 
a  "  step  up  "  transformer  from  low  potential  to  high  poten- 
tial. But  if  the  coil  of  long  thin  wire  be  used  as  the  primary, 
it  becomes  a  "step  down"  transformer  from  high  potential 
to  low  potential. 

If  we  have  a  primary  consisting  of  two  thousand  turns  of 
wire  and  a  secondary  of  one  thousand  turns,  we  get  in  our 
secondary  half  the  voltage  of  the  primary,  but  twice  the 
number  of  amperes.  In  general,  if  we  could  concentrate  all 
the  lines  of  force  of  the  primary  upon  the  secondary  we 
should  have  the  following  relation  :  volts  in  primary  X 
amperes  in  primary  =  volts  in  secondary  X  amperes  in  sec- 
ondary. 

Fig.  468  represents  the  coils  of  a  transformer  used  in  the 
incandescent  lamp  service,  and  Fig.  469  is  the  same  enclosed 
in  a  case.  These  transformers  are  usually  supported  on  the 
street  poles. 

The  transformer  is  applied  in  the  welding  of  metals,  i.e.  to 
fuse  the  ends  of  metals  that  are  to  be  joined  together,  where 
many  hundred  or  even  thousand  amperes  of  current,  and  only 
a  fraction  of  a  volt,  would  be  required  for  an  instant. 


THE   INDUCTION   COIL   REVERSIBLE. 


577 


A  still  wider  application  of  transformers  is  in  the  trans- 
mission of  electric  activity. 

Since  the  rate  at  which  a  current  performs  work  equals 
the  volts  times  the  amperes  (E  X  C),  then  according  to  Ohm's 
law  the  work  done  per  second  by  a  current  passing  through 
a  conductor  equals  C2E  (§  463).  That  is,  when  the  current 


FIG.  468. 


FIG.  469. 


strength  is  doubled  there  will  be  four  times  as  much  energy 
transformed  per  second.  We  see,  then,  that  to  transfer  electric 
energy  to  a  great  distance  it  may  be  desirable  to  have  a  high 
E.M.F.  with  a  small  current  passing  through  the  mains,  and 
then  to  reduce  the  E.M.F.  and  increase  the  current  by  a 
transformer  at  the  place  where  the  energy  is  to  be  used.  By 
this  means  the  expense  involved  in  the  copper  conductors  is 
much  reduced. 

For  electric  lighting  in  private  houses  transformers  are 
used  to  bring  down  the  high  potential  of  the  mains  to  the 
safe  limit  of  about  100  volts. 

The  transformers  may  be  arranged  in  series,  as  shown  in 
Fig.  470,  in  which  case  the  same  primary  current  passes 


578 


ETHER    DYNAMICS. 


through  all  of  them,  and  from  each  secondary  circuit  leads 
may  be  taken  off  to  work  local  lights.     Or  they  may  be 


FlG.  470. 


arranged   in   multiple    arc    (Fig.   471),   in  which   case   each 
primary  current  is  a  bridge  across  from  main  to  main  of  the 


MAIN  CONDUCTOR 


FIG.  471. 


REVERSIBILITY    OF   ELECTROLYSIS.  579 

dynamo  which  supplies  the  alternating  current  of  high 
E.M.F.  In  both  cases  the  secondary  current  would,  if  used 
for  lighting  incandescent  lamps,  be  led  through  lamps  in 
multiple  arc. 


SECTION  XXII. 

SECONDARY    OR    STORAGE    BATTERIES. 

536.  Reversibility  of  electrolysis.  —  If  water  be  decomposed 
for  a  time  between  neutral  electrodes  such  as  platinum  plates 
and  then  the  battery  or  other  generator  be  withdrawn  from 
the  circuit  and  replaced  by  a  sensitive  galvanometer,  a 
deflection  of  the  needle  shows  that  a  transitory  current  flows 
in  the  opposite  direction  to  the  primary  or  electrolyzing  cur- 
rent. It  is  evident  that  the  electrolyzing  current  polarizes 
the  electrodes  in  the  electrolyte,  and  that  energy  is  thus 
stored  in  the  cell.  When  the  wires  are  joined,  this  polariza- 
tion causes  a  current  to  flow  during  an  appreciable  period, 
and  the  •platinum  electrodes  become  depolarized.  The  elec- 
trical energy  of  the  cell  is  converted  into  chemical  potential 
energy  in  that  it  overcomes  the  E.M.F.  of  the  decomposing 
cell.  Polarization  is  of  the  nature  of  a  counter  E.M.F.  It 
is  precisely  this  polarization  which  we  have  to  contend  with 
in  nearly  all  voltaic  cells  (§  437),  and  which  we  seek  to  neu- 
tralize by  means  of  depolarizing  substances. 

Devices  for  thus  storing  up  energy  by  electrolysis,  and 
liberating  it  when  desired  in  the  form  of  electric  current,  are 
called  storage  or  secondary  batteries,  and  sometimes  accumu- 
lators. Note  that  the  process  is  an  electrical  storage  of 
energy,  not  a  storage  of  electricity.  The  energy  assumes 
the  form  of  chemical  potential  energy,  and  there  is  really 
no  more  electricity  in  the  cell  when  it  is  fully  charged  than 
at  the  commencement  of  the  operation. 


580  ETHER    DYNAMICS. 

If,  instead  of  platinum  electrodes,  two  plates  of  lead  cov- 
ered with  a  coating  of  red  lead,  or,  better,  the  positive  plate 
(which  is  the  positive  electrode  when  the  cell  is  being 
charged)  covered  with  a  paste  of  red  lead  and  sulphuric 
acid,  and  the  negative  plate  with  a  paste  of  litharge  and 
sulphuric  acid,  be  used  as  electrodes,  dipping  as  before  into 
sulphuric  acid,  and  the  electrodes  be  connected  with  a  pow- 
erful voltaic  battery  (or,  better,  with  a  dynamo),  the  positive 
electrode  becomes  by  electrolysis  peroxydized  by  the  oxygen 
which  is  liberated,  while  the  negative  is  deoxydized  by  the 
hydrogen.  The  plates  may  remain  in  this  state  for  many 
days.  Hence  the  storage  battery  is  a  very  convenient  means 
of  accumulating  energy  at  one  time  or  place,  and  using  it  at 
some  other  time  or  place.  For  example,  energy  may  be  stored 
during  the  daytime  ;  and  this  energy,  reconverted  into  electric- 
energy,  may  feed  incandescent  lamps  at  night  at  any  conven- 
ient place.  Or  these  batteries,  having  been  charged  by  a 
dynamo,  may  be  transported  to  lecture-halls,  workshops,  elec- 
tric cars,  etc.,  where  powerful  currents  may  be  needed.  The 
E.M.F.  of  these  batteries  may  be  multiplied  many-fold  by 
joining  them  in  series  on  the  same  principle  as  the  E.M.F. 
of  voltaic  batteries  is  increased.  The  E.M.F.  of  a  single  cell 
similar  to  the  above  is  about  2.2  volts.  The  internal  resist- 
ance of  a  cell  whose  surface  of  electrodes  is  300  cm2  is  about 
.006  ohm.  Their  low  resistance  constitutes  one  of  their  chief 
virtues  as  generators.  An  idea  of  the  capability  of  a  storage 
battery  may  be  obtained  from  the  statement  that  a  battery 
capable  of  furnishing  one  horse-power  for  five  hours  weighs 
500  Ibs. ;  it  will  supply  twelve  incandescent  lamps  of  sixteen 
candle-power  each  for  five  hours.  It  will  then  require  to  be 
recharged.  The  great  fault  of  these  accumulators  in  their 
present  form  is  their  want  of  durability. 


ELECTRICAL   TRANSMISSION    OF    ACTIVITY.          581 
SECTION    XXIII. 

ELECTRICAL    TRANSMISSION    OF    ACTIVITY. 

537.  Essentials  for  the  transmission  of  activity  electrically.  — 
The  electrical  transmission  of  activity  (or  power)  demands 
(1)  a  source  of  energy  (e.g.  a  water-power  or  steam  engine) 
and  a  dynamo  ;  (2)  a  line  of  wire  to  serve  as  a  conductor  of 
electricity  ;  and  (3)  a  motor.     The  current  generated  in  the 
dynamo  reaches  the  motor  (which  may  be  many  miles  away) 
and  causes  a  rotation,  and  the  activity  is  communicated  there- 
from to  machinery.    Sometimes  the  circuit  is  metallic  through- 
out, but  often,  as  in  the  case  of  the  electric  railroad,  the  earth 
is  used  in  place  of  a  return  wire. 

538.  Limitations.  —  Activity  of  any  desired  magnitude  may 
be  transmitted,  provided  the  size  of  the  conductor  be  not  too 
small  for  the  current  employed.     The  rate  at  which  energy  j 
is   expended  in  the   motor  is   proportional  to  the  potential 
difference  at  its  terminals,  and  to  the  current  strength.     If 
the  dynamo  give  a  high  potential  difference,  less  current  will 
be   required   to    furnish   a   required   activity.     The    smaller 
current  heats  the  wire  less  (Why  ?     See  Section  VII.) ;  con- 
sequently the  wire  may  be  smaller  as  the  motor  works  at  a 
higher  difference  of  potential.     The   size  of  the  wire  that 
should  be  used   depends  wholly  upon  the   strength  of  the 
current  to  be  transmitted.     For  example,  the  entire  energy  of 
Niagara  Falls  might  be  transmitted  by  an  ordinary  telegraph 
wire  were  it  not  that  the  enormous  potential  difference  re- 
quired would  cause  a  leakage  of  current  at  every  possible 
avenue  of  escape,  and  therefore  make  the  system  a  menace 
to  every  one  near  it. 

539.  Electric  railways.  —  These  furnish  the  most  familial- 
illustrations  of  transmission  of  electric  activity.    The  current 
from  a  dynamo  stationed  at  some  "  electric  plant "  is  conveyed 


582  ETHER    DYNAMICS. 

by  a  trolley  wire  running  along  the  road.  Each  car  carries 
one  or  more  motors,  one  of  whose  terminals  connects  with 
the  trolley  and  the  other  with  the  earth  through  the  wheels 
and  rails.  One  of  the  terminals  of  the  dynamo  is  also  carried 
to  the  earth.  Cars  on  an  electric  railway  are  usually  worked 
in  multiple  arc.  The  trolley  wire  and  the  earth  being  re- 
garded as  parallel  conductors,  the  car  motors  serve  as  bridges 
from  one  to  the  other,  like  the  rungs  of  a  ladder. 

540.  Advantages  of  electrical  transmission  of  activity.     The 
advantages  of  this  method  of  transmission  of  activity  over 
that  by  means  of  belts,  shafts,  compressed  air,  etc.,  are  many 
and  important.     For  example,   it  is   attended  usually  with 
much  less  waste  of  energy.     An  electrical  conductor  is  flex- 
ible ;  it  can  be  bent  and  carried  round  corners  and  tapped 
wherever   wanted.      It   is    motionless,    though   transmitting 
large  quantities  of  energy.     It  transmits  energy  through  very 
long  distances.1 

SECTION   XXIV. 

THERMO-ELECTRIC    CURRENTS. 

541.  Heat  energy  transformed  directly  into  electric  energy. 

Experiment  1.  —  Insert  in  one  screw-cup  of  a  sensitive  galvanometer 
an  iron  wire,  and  in  the  other  cup  a  copper,  or  better,  a  German-silver 
wire.  Twist  the  other  ends  of  the  wire  together,  and  heat  them  at  their 
junction  in  a  flame  ;  a  deflection  of  the  needle  shows  that  a  current  of 
electricity  is  traversing  the  wire.  Place  a  piece  of  ice  at  their  junction  ; 
a  deflection  in  the  opposite  direction  shows  that  a  current  now  traverses 
the  wire  in  the  opposite  direction. 

Experiment  2.  — Take  a  strip  of  sheet  copper  about  15  inches  long 
and  three-fourths  of  an  inch  wide,  and  a  strip  of  zinc  of  the  same  dimen- 

1  In  some  places  in  the  mining  regions  of  the  Western  States  this  is  the  only 
practicable  way  of  supplying  activity  to  the  crushers  and  stamps  of  the  mills.  These 
could  not  be  driven  with  profit  by  steam  engines  on  account  of  the  insurmountable 
difficulties  of  transporting  coal  to  these  localities. 


THERMO-ELECTRIC    CURRENTS.  583 

sions.  Lay  them  one  upon  the  other,  fold  over  each  end  upon  itself  for 
about  half  an  inch,  and  hammer  the  joints  flat,  so  that  they  shall  hold 
together  quite  firmly.  Then  sep- 
arate the  two  strips  into  a  some- 
what elliptical  or  rectangular 
shape,  as  shown  in  Fig.  472. 
Cut  a  hole  through  the  center  of 
one  of  the  strips,  and  pass  the 
wire  support  of  a  magnetic  needle 
through  it.  Place  the  band  in 
the  magnetic  meridian  parallel  Fm-  472' 

with  the  needle.     Direct  a  flame 

against  one  of  the  junctions,  and  note  the  deflection,  and  determine  the 
direction  in  which  the  current  traverses  the  band,  i.e.  whether  the  cur- 
rent -passes  through  the  heated  junction  from  the  copper  or  from  the 
zinc  strip. 

These  currents  are  named,  from  their  origin,  thermo-electric. 
The  apparatus  required  for  the  generation  of  these  currents 
is  very  simple,  consisting  merely  of  bars  of  two  different 
metals  joined  at  one  extremity,  and  some  means  of  raising  or 
lowering  the  temperature  at  their  junction,  or  of  raising  the 
temperature  at  one  extremity  of  the  pair  and  lowering  it  at 
the  other  ;  for  the  electro-motive  force,  and  consequently  the 
strength  of  the  current,  is  nearly  proportional  to  the  differ- 
ence in  temperature  of  the  two  extremities  of  the  pair.  The 
strength  of  the  current  is  also  dependent,  as  in  the  voltaic 
pair,  on  the  thermo-electromotive  force  of  the  metals  em- 
ployed. The  following  thermo-electric  series  is  so  arranged 
that,  if  the  mean  temperature  of  the  two  junctions  be  near 
the  ordinary  temperature  of  the  air,  those  metals  farthest 
removed  from  each  other  give  the  strongest  current  when 
combined ;  and  the  current  passes,  when  they  are  heated  at 
their  junction,  from  the  one  first  named  to  that  succeeding 
it.  The  arrows  indicate  the  direction  of  the  current  at  the 
heated  and  the  cold  ends  respectively.  At  high  temperatures 
the  current  may  be  reversed. 


584 


M 

ETHER    DYNAMICS. 

CoW. 

5 

^ 

-5 

.    s 

s 

I 
pq 

13 
1 

0 

I 

o 

<u         • 

III 

9?      d      *J 

a     '5       ^ 
5-  '  '5     •§ 
Si         C» 

d 
•s 

JS      --       c       o 

,1  ,  yr,  vl  .H 


HEAT 


542.  Thermo-electric  batteries  and  thermopiles.  —  The  E.M.F. 
of  the  thermo-electric  pair  is  very  small  in  comparison  with 
that  of  the  voltaic  pair  ;  hence  the  greater  necessity  of  com- 
bining a  large  number  of  pairs  with  one  another  in  series. 
This  is  done  on  the  same  principle  and  in  the  same  manner 
that  voltaic  pairs  are  united,  viz.  by  joining  the  -(-  metaj  of 
one  part  to  the  —  metal  of  another.  Fig.  473  represents  such 
an  arrangement.  The  light  bars  are  bismuth, 
and  the  dark  ones  antimony.  If  the  source  of 
heat  be  strong  and  near,  one  face  may  be  heated 
much  hotter  than  the  other,  and  a  current  equal 
to  that  from  an  ordinary  galvanic  cell  is  often 
obtained.  Such  contrivances  for  generating 
electric  currents  are  called 
thermo-electric  batteries.  They 
are  seldom  used,  inasmuch  as 
the  best  of  them  transform  less  than  one 
per  cent  of  the  heat  energy  given  out  by 
the  source  of  heat.  Furthermore,  the 
E.M.F.  of  thermic  piles  is  generally  so 
small  that  any  considerable  external  re- 
sistance makes  the  current  extremely  weak. 
If  the  source  of  heat  be  feeble  or  distant, 
the  feeble  current  may  serve  to  measure  the  difference  of  tem- 
perature between  the  ends  of  the  bars  turned  toward  the  heat 
and  the  other  ends,  which  are  at  the  temperature  of  the  air. 
The  apparatus,  when  used  for  this  purpose,  is  called  a  thermo- 
pile or  ther mo-multiplier.  A  combination  (Fig.  474)  of  as 


FIG.  474. 


M  AX  WELL'S  THEORY  OF  LIGHT.  585 

many  as  thirty-six  pairs  of  antimony  and  bismuth  bars,  con- 
nected with  a  very  sensitive  galvanometer,  constitutes  an 
exceedingly  delicate  thermoscope  and  thermometer.  Changes 
of  temperature  that  would  not  produce  a  perceptible  variation 
in  an  ordinary  thermometer  can,  by  the  use  of  a  thermo- 
electric pile,  be  made  to  produce  large  deflections  of  the  galva- 
nometer needle.  Heat  radiated  from  the  body  of  an  insect 
several  inches  from  the  pile  may  cause  a  sensible  deflection. 

SECTION  XXV. 

ELECTRO-MAGNETIC    THEORY    OF    LIGHT.       ELECTRIC    RADIATION. 

543.  Maxwell's  theory  of  light.  —  In  1865  Maxwell  pro- 
pounded the  theory  that  light  is  the  result  of  electro-magnetic 
disturbances  of  rapidly  alternating  character  in  the  ether, 
such  as  would  result  from  its  being  set  in  local  strains  and 
being  released  from  them,  —  that  the  vibrations  which  consti- 
tute light  are  electrical  vibrations,  and  that  light-waves  are 
electrical  or  electro-magnetic  waves. 

Justification  for  this  theory  is  found  in  the  fact  that  elec- 
trical discharges  such  as  that  of  a  Ley  den  jar  have  been 
proven  to  be  oscillatory,  and  give  rise  to  radiations,  i.e. 
ether-waves ;  that  these  radiations  or  electrical  disturb- 
ances travel  with  approximately  the  same  speed  as  light ; 
and  that  they  are  susceptible  of  the  same  changes  and  modi- 
fications as  light.  Furthermore  it  may  be  shown  that  a  mag- 
netic field  may  rotate  the  plane  of  polarization  of  light  and 
an  electrostatic  field  may  change  plane-polarized  into  ellipti- 
cally  polarized  light  and  produce  double  refraction.  These 
modifications  might  be  expected  if  light  itself  consist  of 
electro-magnetic  disturbances. 

The  Maxwellian  theory  of  light  may  now  be  considered  as 
completely  verified  by  the  wonderful  experimental  researches 


586  ETHER    DYNAMICS. 

made  by  the  late  Dr.  Hertz 1  while  a  professor  at  Karlsruhe. 
"  So  that  we  have  now  a  real  midulatory  theory  of  light,  no 
longer  based  on  an  analogy  with  sound,  and  its  inception  and 
early  development  are  among  the  most  tremendous  of  the 
many  achievements  of  the  latter  half  of  the  nineteenth 
century.  The  whole  domain  of  Optics  is  now  annexed  to 
Electricity,  which  has  thus  become  an  imperial  science." 
Lodge. 

The  importance  of  these  experiments  in  a  scientific  sense 
can  scarcely  be  overestimated,  in  so  far  as  they  teach  us  to 
refer  electrostatic  and  electro-magnetic  phenomena  to  the 
intervention  of  the  same  all-pervading  medium.  This  medium 
forms  the  vehicle  by  which  energy  passes  through  space  from 
one  body  to  another,  and  to  which  we  now  must  probably 
look  for  a  knowledge  of  the  process  by  which  one  body  is 
enabled  to  attract  another,  as  well  as  of  facts  concerning  the 
ultimate  constitution  of  matter.  The  term  radiant  energy  is 
continually  acquiring  new  scope  in  physics.2 


1  See  Hertz's  Researches  on  Electrical  Oscillations,  Smithsonian  Report,  1889. 
Hertz  showed  experimentally  that  the  electrical  ether  is  wonderfully  like  if  not 

identical  with  the  ether  which  transmits  light  waves.  By  rapidly  charging  and 
discharging  a  conductor  he  causes  the  ether  upon  it  to  surge  to  and  fro.  This 
agitates  the  surrounding  dielectric  ether,  and  the  disturbance  travels  in  waves.  The 
speed  of  these  waves  he  determines  to  be  the  same  as  the  speed  of  light  waves.  He 
finds  that  these  waves  may  interfere,  be  reflected  from  metal  mirrors,  be  refracted  by 
lenses  and  prisms,  and  are  susceptible  of  diffraction  effects.  He  has  shown  that 
many  optical  experiments  can  be  electrically  performed  by  substituting  dielectrics 
for  transparent  bodies,  and  conductors  for  opaque  bodies. 

2  A  prophecy,    "  The  conclusions  at  which  w%have  arrived,  that  light  is  an  elec- 
trical disturbance,  and  that  light-waves  are  excited  by  electric  oscillations,  must 
ultimately,  and  may  shortly,  have  a  practical  import.     Our  present  systems  of  mak- 
ing light  artificially  are  wasteful  and  ineffective."    (It  is  estimated  that  not  more 
than  5  per  cent  of  the  energy  put  into  an  incandescent  lamp  is  useful  for  illumina- 
tion.)   "We  want  a  certain  range  of  oscillation  between  700  and  400  trillion  vibra- 
tions per  second ;  no  other  is  useful  to  us,  because  no  other  has  any  effect  on  our 
retina ;   but  we  do  not  know  how  to  produce  vibrations  of  this  rate.     .     .     .    We 
want  a  small  range  of  rapid  vibrations,  and  we  know  no  better  than  to  make  the 
whole  series  leading  up  to  them.     It  is  as  though,  in  order  to  sound  some  little  shrill 
octave  of  pipes  in  an  organ,  we  were  obliged  to  depress  every  key  and  every  pedal* 
and  to  blow  a  young  hurricane.    .     .    . 


descent  electric  lights,  only  I. 

SECTION  XXVI. 

SOME    USEFUL    APPLICATIONS    OF    ELECTRIC    ENERGY.— 
ELECTRIC    LIGHT. 

The  applications  of  electric  energy  to  industrial  uses  are 
so  numerous  and  varied  that  the  limits  of  an  ordinary  text- 
book on  general  Physics  can  do  little  justice  to  the  subject, 
and,  indeed,  a  description  of  the  various  appliances  in  use  is 
of  too  technical  a  character  to  come  properly  within  the 
scope  of  a  school  or  college  course.  Public  libraries  are  now 
well  provided  with  popular  works  relating  to  every  industrial 
application. 

544.  Electric  light :  voltaic  arc.  —  If  the  terminals  of  wires 
from  a  powerful  dynamo  or  galvanic  battery  be  brought  to- 
gether, and  then  separated  1  or  2  mm,  the  current  does  not 
cease  to  flow,  but 
volatilizes  a  portion 
of  the  terminals.  The 
vapor  formed  be- 
comes a  conductor  of 

high  resistance,  and, 

FIG.  475. 
remaining  at  a  very 

high  temperature,  produces  intense  light.     The  light  rivals 

"  Any  one  looking  at  a  common  glow-worm  must  be  struck  with  the  fact  that  not 
by  ordinary  combustion  nor  yet  on  the  steam-engine  and  dynamo  principle  is  that 
easy  light  produced.  Very  little  waste  radiation  is  there  from  phosphorescent  things 
in  general."  (Prof.  Langley  has  found  that  light  of  one  candle-power  from  a  Cuban 
firefly  can  be  produced  by  an  expenditure  of  one  four-hundredth  of  the  energy 
required  for  a  one-candle-power  gas  jet.)  .  .  . 

"  Solar  radiation  consists  of  Avaves  of  all  sizes,  it  is  true  ;  but  solar  radiation  has 
innumerable  things  to  do  besides  making  things  visible.  The  whole  of  its  energy  is 
useful.  In  artificial  lighting  nothing  but  light  is  desired  ;  when  heat  is  Avanted  it  is 
best  obtained  separately,  by  combustion.  So  soon  as  we  clearly  recognize  that  light 
is  an  electrical  vibration,  so  soon  shall  we  begin  to  beat  about  for  some  mode  of 
fexciting  and  maintaining  an  electrical  vibration  of  any  required  degree  of  rapidity. 
When  this  has  been  accomplished,  the  problem  of  artificial  lighting  will  have  been 
solved."  Lodge.  The  production  of  light  by  very  rapidly  alternating  currents 
seems  to  some  to  give  promise  of  success  in  this  direction  (see  Section  XXXI). 


588 


ETHER   DYNAMICS. 


that  of  the  sun  both  in  intensity  and  whiteness.  The  heat  is 
so  great  that  it  fuses  the  most  refractory  substances.  Metal 
terminals  quickly  melt  and  drop  off  like  tallow,  and  thereby 
become  so  far  separated  that  the  electro-motive  force  is  no 
longer  sufficient  for  the  increased  re- 
sistance, and  the  light  is  extinguished. 
Hence,  pencils  of  carbon  (prepared 
from  the  coke  deposited  in  the  distilla- 
tion of  coal  inside  of  gas  retorts),  be- 
ing less  fusible,  are  used  for  terminals. 
For  simple  experiments  these  pencils 
may  be  held  in  forceps  (Fig.  475)  at 
the  ends  of  two  brass  rods,  to  which 
the  battery  wires  are  attached.  These 
rods  slide  in  brass  heads,  A  and  B, 
supported  by  insulating  pillars,  so  that 
the  distance  between  the  carbon  points 
may  be  regulated. 

The  light  is  too  intense  to  admit  of 
examination  with  the  naked  eye ;  but 
if  an  image  of  the  terminals  be  thrown 
on  a  screen  by  means  of  a  lens  or  a 
pin-hole   in   a   card,    an    arch-shaped 
light  is  seen  extending  from  pole   to 
pole,  as  shown  in  Fig.  476. 
The  heated  air  containing  the  glowing  particles  of  carbon 
forms  what  is  called  the  electric  arc. 

The  larger  portion  of  the  light,  however,  emanates  from 
the  tips  of  the  two  carbon  terminals,  which  are  heated  to  an 
intense  whiteness,  although  some  emanates  from  the  arc. 
The  +pole  is  hotter  than  the  —pole,  as  is  shown  by  its 
glowing  longer  after  the  current  is  stopped.  The  carbon  of 
the  -|-pole  becomes  volatilized,  and  the  light-giving  particles 
are  transported  from  the  -fpole  to  the  —pole,  forming  a 


FIG.  476. 


ELECTRIC    LAMPS. 


589 


bridge  of  luminous  vapor  between  the  poles.  What  we  see  is 
not  electricity,  but  luminous  matter. 

The  light  of  the  ordinary  street  arc-lamp  has  an  intensity 
varying  from  one  to  two  thousand  candle-power,  or  the  com- 
bined intensity  of  from  fifty  to  a  hundred 
ordinary  gas-lights.  To  sustain  such  a  light, 
about  one  horse-power  per  lamp  must  be  ap- 
plied at  the  dynamo. 

545.  Electric  lamp.  —  It  is  apparent  that 
the  -{-pole  is  subject  to  a  wasting  away ;  so 
also  the  — pole  wastes  away,  but  not  so  fast. 
At  the  point  of  the  former  a  conical-shaped 
cavity  is  formed,  while  around  the  point  of 
the     latter     warty     protuberances     appear. 
When,  in  consequence  of  the  wearing  away 
of  the  -|-  pole,  the  distance  between  the  two 
pencils    becomes  too  great  for   the   electric 
current  to  span,  the  light  goes  out.     Numer- 
ous self-acting  regulators  for  maintaining  a 
uniform   distance   between   the    poles    have 
been  devised.      Such  an  arrangement  (Fig. 
477)  is  called  an  electric  lamp.     The  move- 
ments of  the  carbons  are  accomplished  auto- 
matically by  the  action  of  the  current  itself. 

The  difference  between  the  arc-lamps  of 
the  various  inventors  is  a  difference  in  the 
mode  of  adjusting  or  "  feeding  "  the  carbons. 
We  give  on  the  following  page  the  plan  of  the 

546.  Brush  lamp.  —  The  current,  entering 
at  A  (Fig.  478),  divides  at  B  into  two  branches, 

which  pass  around  the  bobbin  C  in  opposite  directions,  one 
branch  being  a  coarse  wire  of  low  resistance  and  in  the  same 
circuit  as  the  carbons,  and  the  other  branch,  S  S,  being  a 
shunt  of  high  resistance,  connecting  the  terminals  B  and  G. 


FIG.  477. 


590 


ETHER    DYNAMICS. 


FIG.  478. 


Inside  the  bobbin  is  a  soft  iron  core,  F,  which  is  attached  to 
the  upper  carbon.  When  a  current  passes  through  the  two 
G  branch  circuits  on  the  bobbin  C,  they 
tend  to  magnetize  the  core  in  op- 
posite directions,  but  the  resistances 
and  number  of  turns  in  the  two  cir- 
cuits are  so  proportioned  that  the 
magnetic  field  due  to  the  low  resist- 
i  ance  branch  is  the  stronger,  and  the 
I  core  F  is  therefore  drawn  up  into  the 
bobbin,  lifting  the  upper  carbon  and 
establishing  the  arc.  Should  the  car- 
bons become  too  widely  separated, 
the  resistance  of  the  arc,  and  con- 
sequently of  the  coarse  wire  circuit 
on  C,  increases,  diminishing  the  cur- 
rent in  C  and  increasing  that  in  the  shunt  S.  The  field  due 
to  the  shunt  is  therefore  strengthened)  and  that  due  to  the 
coarse  wire  diminished,  allowing  the  core 
F  to  fall  slightly,  bringing  the  carbons 
nearer  together.  By  the  device  of  the 
two  opposing  fields,  due  to  the  coils  on 
C  being  wound  in  opposite  directions, 
the  feeding  of  the  lamp  is  done  auto- 
matically, and  the  actual  distance  of  the 
two  carbons  varies  but  little. 

547.  Incandescent  electric  lamps. — The 
incandescent  (or  "  glow ")  light  is  pro- 
duced by  the  heating  of  some  refractory 
body  to  a  state  of  incandescence  by  the 
passage  of  an  electric  current.  Carbon 
filaments  are  now  almost  exclusively 
used  in  incandescent  lamps.  The  fila- 
ment of  the  Edison  lamp  is  carbonized  bamboo.  It  is  essential 


INCANDESCENT   ELECTRIC   LAMPS. 


591 


that  the  oxygen  of  the  air  be  removed  from  these  bulbs,  other- 
wise the  carbons  would  be  quickly  burned  out ;  hence  very 
high  vacua  are  produced  in  the  bulbs  with  a  mercury  pump. 

Fig.  479  represents  an  Edison  lamp.  The*  loop  or  filament 
of  carbon,  L,  is  joined  at  n  n  to  two  platinum  wires  which  pass 
through  the  closed  end  of  the  glass  tube,  T.  One  of  these  wires 
is  connected  with  the  brass  ring,  B,  and  the  other  with  the 
brass  button,  D,  at  the  bottom  of  the  lamp.  When  the  lamp 
is  screwed  into  its  socket,  connection  is  made  with  the  line 
through  pieces  of  brass  in  the  socket  which  are  insulated 
from  each  other. 

An  Edison  16  candle-power  lamp  has  a  resistance  (when 
hot)  of  about  140  ohms,  the  difference  of  potential  at  its 
terminals  is  about 
110  volts,   and   it 
requires  a  current 
of     0.75     ampere. 
Each     lamp     con- 
sumes  about  one- 
tenth  of  a  horse- 
power. 

Incandescent 
lamps  are  usually 
introduced  into  the  circuit  in  multiple  arc  (Fig.  480),  the 
current  being  equally  divided  by  properly  regulating  the 
resistance  between  all  the  lamps  in  the  circuit. 

The  customer  pays  by  the  watt-hour l  for  the  electric  energy 

1  A  watt  of  electrical  activity  corresponds  to  7J5  h.p.  of  mechanical  activity ; 
hence,  if  a  lamp  or  motor  take  activity  equivalent  to  ^  h.p.  for  one  hour,  it  con- 
sumes one  watt-hour  of  energy,  or  3600  joules. 

It  has  been  found  that  an  incandescent  lamp  consuming  1000  watt-hours  of  elec- 
trical activity  gives  about  one-tenth  of  the  illumination  given  by  1000  feet  of  gas  under 
ordinary  circumstances  ;  consequently,  in  order  that  the  customer  may  pay  for  elec- 
tric light  at  the  same  proportional  rate  for  the  same  illumination  that  he  would  pay 
for  gas,  the  price  per  thousand  watt-hours  must  be  placed  at  one-tenth  of  the  price 
per  thousand  feet  of  gas. 


FIG.  480. 


592 


ETHER   DYNAMICS. 


PROM  GENERATOR 


consumed  ;  a  watt-hour  being  the  energy  expended  in   one 
hour  when  the  activity  is  one  watt.     A  16  c.p.  lamp  con- 

The  following  are  tabulated  results  of  measurements  of  incandescent  lamps,  made 
at  Paris  (1892): 


"3  <a 

.£2=5 

8 

a:  3 

e'c  * 

c 
II 

Electric  Activity 

fcsJ 

No.  of 

Lamp. 

c.  --> 

sin 

fill 

III- 

K    O 

£  S« 
III 
Q'S.S 

B 

£J| 

-slw 

•Ss^ 

S5S. 

Lamps 
per  H.P. 

II 

Watts. 

H.P. 

Edison  A  .  . 

16 

15.38 

137.4 

89.11 

.651 

57.98 

.0788 

196.4 

12.28 

"       B.. 

32 

31.11 

130.03 

98.39 

.758 

74.62 

.0941 

307.25 

9.60 

Swan  A  

16 

1661 

32.78 

47.30 

1.471 

69.24 

.0945 

177.92 

11.12 

"     B  

32 

32.21 

31.75 

54.21 

1.758 

94.88 

.1059 

262.49 

8.20 

ELECTKOTYPING.  593 

sumes  about  75  watts,  or  about  4.7  watts  per  candle.  A  great 
many  meters  have  been  devised  for  registering  the  electrical 
energy  consumed.  Some  of  them  are  virtually  small  electric 
motors,  which  revolve  at  varying  speed  according  to  the 
strength  of  the  current  and  record  the  total  number  of  revo- 
lutions per  month,  somewhat  as  is  done  in  a  gas  meter. 

Fig.  481  represents  such  a  meter.  In  the  upper  part  of 
the  figure  is  seen  a  coil  within  two  coils.  This  coil  is  fixed  to 
a  vertical  axle  and  is  caused  to  revolve  by  the  tendency  of 
a  current  to  intersect  the  lines  of  magnetic  force  developed  by 
the  outer  coils.  In  the  lower  part  of  the  figure  is  seen  a 
circular  copper  disk  attached  to  the  same  axis  with  the  coil 
and  caused  by  it  to  revolve  between  the  poles  of  powerful 
permanent  magnets.  This  rotation  in  the  magnetic  field 
develops  induced  currents  in  the  disk,  and  the  interaction 
between  these  currents  and  the  amperian  currents  of  the 
magnets  causes  a  "drag"  upon  the  rotation  so  that  the  speed 
of  rotation  is  thus  diminished.  As  has  already  been  stated 
(§  464)  the  Edison  meter  is  an  electrolytic  coulomb  meter. 


SECTION   XXVII. 

USEFUL     APPLICATIONS     OF     ELECTRICITY     CONTINUED.  — 
ELECTROTYPING     AND     ELECTROPLATING. 

548.  Electrotypiny.  —  This  book  is  printed  from  electro- 
type plates.  A  moulding-case  of  brass,  in  the  shape  of  a 
shallow  pan,  is  filled  to  the  depth  of  about  one-quarter  of  an 
inch,  with  melted  wax.  A  few  pages  are  set  up  in  common 
type,  and  an  impression  or  mold  is  made  by  pressing  these 
into  the  wax.  The  type  is  then  distributed,  and  again  used 
to  set  up  other  pages.  Powdered  plumbago  is  applied  by 
brushes  to  the  surface  of  the  wax  mold  to  render  it  a  con- 
ductor. The  case  is  then  suspended  in  a  bath  of  copper 


594 


ETHER    DYNAMICS. 


sulphate  dissolved  in  dilute  sulphuric  acid.  The  —  pole  of 
a  galvanic  battery  or  dynamo  machine  is  applied  to  it ;  and 
from  the  -f-  pole  is  suspended  in  the  bath  a  copper  plate 
opposite  and  near  to  the  wax  face.  The  salt  of  copper  is 
decomposed  by  the  electric  current,  and  the  copper  is  deposited 
on  the  surface  of  the  mold.  The  sulphuric  acid  appears  at 
the  -|-pole,  and,  combining  with  "the  copper  of  this  pole, 


FIG.  482 


forms  new  molecules  of  copper  sulphate.  When  the  copper 
film  has  acquired  about  the  thickness  of  an  ordinary  visiting 
card,  it  is  removed  from  the  mold.  This  shell  shows  dis- 
tinctly every  line  of  the  types  or  engraving.  It  is  then 
backed,  or  filled  in,  with  melted  type-metal,  to  give  firmness 
to  the  plate.  The  plate  is  next  fastened  on  a  block  of  wood, 
and  thus  built  up  type-high,  and  is  now  ready  for  the  printer. 
(For  full  directions  which  will  enable  a  pupil  to  electrotype 
in  a  small  way,  see  the  author's  Physical  Technics.) 

549.  Electroplating.  — The  distinction  between  electroplat- 
ing and  electrotyping  is  that  with  the  former  the  metallic 
coat  remains  permanently  on  the  object  on  which  it  is 


THE   TELEGRAPH.  595 

deposited,  while  with  the  latter  it  is  intended  to  be  removed. 
The  processes  are,  in  the  main,  the  same.  The  articles  to  be 
plated  are  first  thoroughly  cleaned  and  suspended  on  the 
—  pole  of  a  battery,  and  then  a  plate  of  the  same  kind  of 
metal  that  is  to  be  deposited  on  the  given  articles  is  sus- 
pended from  the  -f-pole  (Fig.  482).  The  bath  used  is  a 
solution  of  a  salt  of  the  metal  to  be  deposited.  The  cyanides 
of  gold  and  silver  are  generally  used  for  gilding  and  silvering. 
Many  of  the  base  metals  require  to  be  electro-coppered  first, 
in  order  to  secure  the  adhesion  of  the  gold  or  silver.  The 
dynamo  has  almost  completely  replaced  the  voltaic  battery 
for  electrotyping  and  electroplating  purposes. 


SECTION  XXVIII. 

USEFUL    APPLICATIONS    OF    ELECTRIC    ENERGY    CONTINUED.  — 
TELEGRAPHY. 

550.  The  telegraph.  — The  word  telegraph  literally  signifies 
to  write  far  away.  In  its  broadest  sense  it  embraces  all 
methods  of  communicating  thought  with  great  speed  to  a 
distance,  by  means  of  intelligible  characters,  sounds  or  signs  ; 
but  usually  it  is  applied  only  to  electrical  methods. 

First,  it  should  be  understood  that,  instead  of  two  lines  of 
wires  (one  to  convey  the  electric  current  far  away  from  the 
battery,  and  another  to  return  it  to  the  battery),  if  the  distant 
pole  be  connected  with  a  large  metallic  plate  buried  in  moist 
earth,  or,  still  better,  with  a  gas  or  water  pipe  that  leads  to 
the  earth,  and  the  other  pole  near  the  battery  be  connected 
in  like  manner  with  the  earth,  so  that  the  earth  forms  about 
one-half  of  the  circuit,  there  will  be  needed  only  one  wire  to 
connect  telegraphically  two  places  that  are  distant  from  each 
other.  Furthermore,  the  resistance  offered  by  the  earth  to 
the  electric  current  is  practically  nothing  ;  so  that,  disregarding 


596 


ETHER    DYNAMICS. 


the  Resistance  of  the  ground  connections,  there  is  a  saving  of 
one-half  the  wire  and  nearly  oner-half  the  resistance,  and  con- 
sequently of  about  one-half  the  battery  power. 

Let  B  (Fig.  483,  Plate  IV)  represent  the  message  sender, 
or  operator's  key  ;  Y,  the  message  receiver.  It  may  be  seen 
that  the  circuit  is  broken  at  B.  Let  the  operator  press  his 
finger  on  the  knob  of  the  key.  He  closes  the  circuit,  and  the 
electric  current  instantly  fills  the  wire  from  Boston  to  New 
York.  It  magnetizes  a ;  a  draws  down  the  lever  b,  and 
presses  the  point  of  a  style  on  a  strip  of  paper,  c,  that  is 
drawn  over  a  roller.  The  operator  ceases  to  press  upon  the 
key,  the  circuit  is  broken,  and  instantly  b  is  raised  from  the 
paper  by  a  spiral  spring,  d.  Let  the  operator  press  upon 
the  key  only  for  an  instant,  or  long  enough  to  count  one  :  a 
simple  dot  or  indentation  will  be  made  in  the  paper.  But  if 


FIG.  484. 

he  press  upon  the  key  long  enough  to  count  three,  the  point 
of  the  style  will  remain  in  contact  with  the  paper  the  same 
length  of  time  ;  and,  as  the  paper  is  drawn  along  beneath  the 
point,  a  short  straight  line  is  produced.  This  short  line  is 
called  a  dash.  These  dots  and  dashes  constitute  the  alphabet 
of  telegraphy.  For  instance,  a  part  of  a  message,  "  man  is  in," 


THE    SOUNDER.  597 

is  represented  as  printed  in  telegraphic  characters  on  the  strip 
of  paper.  The  Roman  letters  above  interpret  their  meaning. 
Fig.  484  represents  the  Morse  telegraph  receiver  in  actual 
use. 

551.  The  sounder.  — If  the  strip  of  paper  be  removed,  and 
the  style  be  allowed  to  strike  the  metallic  roller,  a  sharp  click 
is  heard.     Again,  when  the  lever  is  drawn  up  by  the  spiral 
spring  it  strikes  a  screw  point  above  (not  represented  in  the 
figure),  and  another  click,  differing  slightly  in  sound  from  the 
first,  is  heard.     A  listener  is  able  to  distinguish  dots  from 
dashes  by  the  length  of  the  intervals  of  time  that  elapse  be- 
tween these  two  sounds.     Operators  generally  read  by  ear, 
giving  heed  to  the  clicking  sounds  produced  by  the  strokes 
of  a  little  hammer.     A  receiver  so  used  is  called  a  sounder,  a 
common  form  of  which  is  represented  in  the  lower  central 
part  of  Plate  IV. 

552.  The  relay  and  the  repeater.  —  The   strength  of  the 
current  is  diminished,  of  course,  as  the  line  is  extended  and 
the  number  of  instruments  in  the  circuit  is  increased.     Hence, 
a  battery  that  would  give  a  current   sufficient  to  move  the 
parts  of  a  single  sounder  audibly,  on  a  short  line,  would  not 
move  the  same  parts  of  many  sounders  on  a  long  line  with 
sufficient  force  to  render  the  message  audible.     Kesort  is  had 
to  relays  and  repeaters. 

In  Fig.  485,  Plate  IV,  R  represents  a  relay  and  S  a  sounder. 
Suppose  a  weak  current  arrives  at  New  York  from  Boston, 
and  has  sufficient  strength  to  attract  the  armature  of  the  relay 
at  that  station.  This,  as  may  be  seen  by  examination  of  the 
diagram,  will  close  another  short  circuit,  called  the  local 
circuit,  and  send  a  current  from  a  local  battery  located  in 
the  same  office  through  the  sounder  at  that  station.  The 
sounder,  being  operated  by  a  battery  in  a  circuit  of  only  a 
few  feet  in  length,  delivers  the  message  audibly.  If  it  be 
desired  that  the  message  should  go  beyond  New  York,  —  for 


598  ETHER   DYNAMICS. 

instance,  to  Philadelphia,  —  then  we  have  only  to  suppose 
the  local  line  at  New  York  to  be  lengthened  so  as  to  extend 
to  Philadelphia,  and  a  powerful  line  battery  to  be  substituted 
for  the  small  local ;  then  the  message  that  leaves  Boston  will 
be  shifted  from  one  circuit  to  the  other  at  New  York,  and  be 
delivered  in  Philadelphia  without  the  intervention  of  any 
operator  on  the  route.  In  this  case  a  relay  is  called  a  re- 
peater. The  electro-magnets  in  relays  are  wound  with  long, 
thin  wire,  while  those  of  sounders  are  wound  with  short, 
large  wire.  The  main  battery  consists  of  many  cells  in  series. 
It  may  be  located  at  either  terminus,  but  it  is  generally  split 
in  halves,  and  one  half  is  placed  at  each  terminus. 

In  the  diagram  the  circuit  is  represented  as  open  at  both 
keys.  When  the  line  is  not  in  use,  the  circuit  ought  always  to 
be  left  closed,  by  means  of  switches  connected  with  the  keys 
(not  represented  in  the  diagram),  so  that  when  the  line  is  not 
"at  work"  an  electric  current  is  constantly  traversing  the 
wire.  Sending  a  message,  consequently,  consists  in  inter- 
rupting this  current  by  means  of  a  key.  Suppose  that  Boston 
wishes  to  communicate  with  New  York.  He  first  removes 
the  switch  on  his  key,  which  breaks  the  circuit  and  enables 
him  to  control  the  circuit  with  his  key.  He  then  manipulates 
his  key  so  as  to  produce  an  understood  signal,  which  will 
attract  New  York's  attention.  Every  time  that  Boston  presses 
on  his  key,  every  armature  in  his  own  office,  and  in  the  New 
York  office,  and  at  way  stations,  falls.  Of  course  the  message 
may  be  read  at  every  station  on  the  route. 


TELEGRAPHIC    ALPHABET.  599 

TELEGRAPHIC    ALPHABET. 


A 

B 

C 

D 

E 

F 

7 

H 

I 

J 

K 

L 

M 

N 

0 

P 

Q 

R 

S 

> 

u 

V 

w 

^"Dv      r^ 

Y 

Z 

& 

1 

? 

TELEGRAPHIC   FIGURES. 
12345  6 

7890 
SECTION  XXIX. 

USEFUL    APPLICATIONS    OF    ELECTRIC    ENERGY    CONTINUED.— 
TELEPHONY. 

553.  Bell  telephone.  —  Fig.  486  represents  a  sectional  and 
a  perspective  view  of  this  instrument.  It  consists  of  a  steel 
magnet,  A,  encircled  at  one  extremity  by  a  spool,  B,  of  very 
fine  insulated  wire,  the  ends  of  which  are  connected  with  the 
binding  screws,  D  D.  Immediately  in  front  of  the  magnet  is 
a  thin  circular  iron  disk,  E  E.  The  whole  is  enclosed  in  a 
wooden  or  rubber  case,  F.  The  conical-shaped  cavity,  G, 
serves  the  purpose  of  either  a  mouth-piece  or  an  ear-trumpet. 
There  is  no  difference  between  the  transmitting  and  the  re- 
ceiving telephone ;  consequently,  either  instrument  may  be 
employed  as  a  transmitter,  while  the  other  serves  as  a  re- 
ceiver. Two  magneto-telephones  in  a  circuit  are  virtually 


600 


ETHER    DYNAMICS. 


in  the  relation  of  a  dynamo  and  a  motor.  The  transmitter 
being  in  itself  a  diminutive  dynamo,  of  course  no  battery  is 
required  in  the  circuit.  Connect  in  circuit  two  such  tele- 
phones, and  the  apparatus  is  ready  for  use. 

When  a  person  talks  near  the  disk  of  the  transmitter,  he 
throws  it  into  rapid  vibration.  The  disk,  being  quite  close 
to  the  magnet,  is  magnetized  by  induction  ;  and  as  it  vibrates, 
its  magnetic  power  is  constantly  changing,  being  strengthened 


FIG.  486. 


as  it  approaches  the  magnet,  and  enfeebled  as  it  recedes. 
This  fluctuating  magnetic  force  will  of  course  induce  currents 
in  alternate  directions  in  the  neighboring  coil  of  wire.  These 
currents  traverse  the  whole  length  of  the  wire,  and  so  pass 
through  the  coil  of  the  distant  instrument.  When  the  direc- 
tion of  the  arriving  current  is  such  as  to  increase  the  intensity 
of  the  magnetic  field  of  the  receiver,  the  magnet  attracts  the 
iron  disk  in  front  of  it  more  strongly  than  before.  When  the 
current  is  in  the  opposite  direction,  the  disk  is  less  attracted, 
and  flies  back.  Hence  the  disk  of  the  receiving  telephone  is 


BELL    TELEPHONE. 


601 


forced  to  repeat  whatever  movement  is  imparted  to  the  disk 
of  the  transmitting  telephone.  The  vibrations  of  the  former 
disk  become  sound  in  the  same  manner  as  the  vibrations  of  a 
tuning-fork  or  of  the  head  of  a  drum. 

The  above  is  a  description  of  the  original  and  simplest 
form  of  the  Bell  telephone.  It  is  apparent  that  the  original 
energy  (i.e.  that  of  the  voice)  applied  at  the  transmitter 
must,  during  its  successive  transformations  and  especially 


FIG.  487. 


FlG.  488. 

during  its  transmission  in  the  form  of  electric  energy  through 
large  resistances,  become  very  much  enfeebled,  so  that  when 
it  reappears  as  sound,  the  sound  is  quite  feeble  and  frequent- 
ly inaudible.  The  first  grand  improvement  on  the  original 
consists  in  introducing  a  battery  into  the  circuit,  and  so 
arranging  that  the  voice,  instead  of  being  obliged  to  generate 
currents,  shall  be  required  to  act  only  as  the  controlling  force 
of  a  current  already  generated  by  the  battery.  It  is  evident 
that  only  a  fluctuating  or  undulating  current  can  produce  the 


602 


ETHER   DYNAMICS. 


necessary  vibrations  in  the  disk  of  the  receiver.  The  fluctua- 
tions are  caused  by  a  varying  resistance  in  the  circuit.  The 
pupil  must  have  learned  by  experience  ere  this  that  the  effect 
of  a  loose  contact  between  any  two  parts  of  a  circuit  is  to 
increase  the  resistance  and  thereby  weaken  the  current ;  but 
the  effect  of  a  slight  variation  in  pressure  is  especially  notice- 
able when  either  or  both  of  the  parts  are  carbon.  Fig.  487 
illustrates  a  simple  telephonic  circuit  in  which  are  included 
a  variable  resistance  transmitter  T,  a  magneto-receiver  E. 
and  a  battery  B.  One  of  the  electrodes,  a  platinum  point, 
touches  the  center  of  the  transmitter  disk ;  the  other  electrode, 
a  carbon  button  a,  is  pressed  by  a  spring  gently  against  the 
platinum  point.  Every  vibration  of  the  disk,  however 
minute,  causes  a  variation  in  the  pressure  between  the  two 
electrodes  and  a  corresponding  variation  in  the  circuit  resist- 
ance. As  the  resistance  changes,  so  changes  the  current 
strength,  and  so  consequently  changes  the  force  with  which 
the  magnet  in  the  receiver  E  pulls  its  disk.  The  varying 
tension  between  magnet  and  disk  causes  the  latter  to  vibrate 
and  reproduce  sounds. 

The  next  improvement  of  considerable  importance  consists 
in  the  adoption  of  an  induction  coil,  which,  we  have  learned, 
produces  a  current  of  much  greater  electro-motive  force  than 
is  possessed  by  the  original  battery  current.  By  its  adoption 
we  are  able  to  converse  over  much  longer  distances,  and  since 
the  battery  current  traverses  only  a  local  circuit,  as  may  be 
seen  by  reference  to  Fig.  488,  a  single  Leclanche  cell  is  gener- 
ally sufficient  to  operate  it.  The  currents  induced  by  the 
fluctuating  primary  current  traverse  the  line  wire  and  generate 
sonorous  vibrations  in  the  disk  of  the  receiver  in  the  same 
manner  as  in  the  original  telephone. 

Fig.  489  represents  the  entire  telephonic  apparatus  required 
at  any  single  station.  The  box  A  contains  a  small  hand- 
dynaruo,  such  as  is  represented  in  Fig.  490.  A  person  turn- 


MICROPHONE. 


603 


ing  the  crank  F  generates  a  current  which  rings  a  pair  of 
electric  bells  G,  both  at  his  own  and  at  a  distant  station,  and 


FIG.  490. 

thus  attracts  attention.  He  next  takes 
the  receiver  B  off  the  supporting  hook 
and  places  it  at  his  ear.  When  the 
weight  is  removed  from  the  hook,  the 
hook  rises  a  little  and  throws  the 
dynamo  and  bells  out  of  the  circuit, 
and  at  the  same  time  introduces  the 
receiver  B,  the  transmitter  C,  and  the 
battery  D,  so  that  the  circuit  stands 
as  represented  in  Fig.  488.  The  box 
C  contains  the  induction  coil.  E  is  a 
"lightning  arrester." 

554.  Microphone.  —  In  Fig.  491  A 
and  B  are  buttons  of  carbon ;  the  for- 
mer is  attached  to  a  sounding-board 
of  thin  pine  wood,  the  latter  to  a 
steel  spring  C,  and  both  are  connected  in  circuit  with  a 
battery  and  a  telephone  used  as  a  receiver.  The  spring 
presses  B  against  A,  and  any  slight  jar  will  cause  a  variation 
in  the  pressure  and  corresponding  variations  in  the  current 
strength. 

By  means  of  this  instrument,  called  the  microphone,  any 
little  sound  (as  its  name  indicates)  such  as  the  ticking  of  a 


FIG.  489. 


604 


ETHER   DYNAMICS. 


watch  or  the  footfall  of  an  insect  may  be  reproduced  at  a 
considerable  distance,  and  be  as  audible  as  though  the 
original  sounds  were  made  close  to  the  ear. 


A.. 


FIG.  491. 

555.    Bell's  photophone  or  radiophone. 

This  is  an  instrument  by  means  of  which  sound-waves  may  be 
generated  by  rays  of  light,  and  speech  be  transmitted  through  the 
instrumentality  of  ether-vibrations.  Rays  of  light  of  the  sun,  an 
electric  lamp,  etc.  fall  upon  a  mirror  M  (Fig.  492)  and  are  reflected 
to  a  disk  D  of  silvered  mica.  A  person  speaking  into  0  causes  the 

disk  to  vibrate,  and 
this  causes  corre- 
sponding condensa- 
tions and  rarefac- 
tions of  the  incident 
ether  -  waves.  The 
ether-waves  are  re- 
flected from  the 
silvered  disk  and 

FlG  492  fall  upon  a  distant 

parabolic  mirror  R 
and  are  reflected  thence  upon  a  selenium  cell  P.     This  cell  is  there- 


THE   ELECTRIC    FIRE-ALARM. 


605 


fore  exposed  to  an  undulatory  radiation  corresponding  to  the 
sound- vibrations.  The  conductivity  of  selenium  is  susceptible  to 
rapid  changes  caused  by  slight  changes  of  radiant  energy  falling 
upon  it.  Hence  a  current  from  a  battery  B  passing  through  the 
cell  P  and  telephone  receiver  T  is  transformed  into  an  undulatory 
current  corresponding  to  the  undulatory  radiations  received  by  the 
cell.  The  undulatory  current  causes  the  disk  of  the  receiver  T  to 
emit  sound-waves  which  are  audible  to  the  ear. 

Mercadier,  by  introducing  a  cell  C  containing  a  solution  of 
iodine  which  has  the  property  of  absorbing  light-bearing  waves, 
found  that  the  results  were  not  affected  thereby.  He  therefore 
concluded  that  light-giving  radiations  are  not  essential  to  the  suc- 
cessful operation  of  this  apparatus,  and  consequently  gave  it  the 
more  appropriate  name  of  radiophone. 

556.    The  electric  fire-alarm. 

This  is  a  modification  of  the  electro-magnetic  telegraph.  Fig. 
493  will  serve  to  illustrate  the  general  plan  of  the  American  system, 


FIG.  493. 

invented  by  Prof.  M.  G.  Fanner,  and  by  him  first  introduced  into 
Boston  in  the  year  1852. 

From  some  central  station  wires  radiate  to  every  part  of  the 
city.  At  suitable  intervals  there  are  inserted  in  these  circuits  small 
cottage-shaped  boxes,  usually  attached  to  buildings  at  the  corners 
of  streets.  On  opening  one  of  these  boxes,  a  person  who  is  to  give 


606  ETHER    DYNAMICS. 

an  alarm  finds  a  crank  A,  which  he  is  directed  to  "pull  down  once 
and  let  go."  This  winds  the  spring  H,  which  sets  in  motion  a 
tram  of  wheels,  and  causes  a  make-and-break  wheel  C  to  revolve. 
This  wheel  bears  upon  its  circumference  notches  corresponding  to 
the  number  of  the  box.  Two  terminals  of  the  line  are  so  con- 
nected, one  with  C  and  the  other  with  a  lever  6,  that  when  the 
lever  touches  the  wheel  the  circuit  is  closed.  But  when  the  wheel 
revolves,  and  a  notch  passes  under  the  lever,  the  circuit  is  broken. 
The  effect  of  breaking  the  circuit  is  to  demagnetize  the  electro- 
magnet F  at  the  central  station,  and  release  the  armature,  which  is 
attached  to  the  tongue  of  a  bell.  The  tongue,  being  then  drawn 
forcibly  by  the  spring  G  in  the  opposite  direction,  produces  one 
stroke  on  the  bell.  By  pulling  the  lever  down  once,  the  spring  is 
wound  up  just  enough  to  cause  C  to  revolve  three  times,  and  thus 
the  number  of  the  box  is  struck  three  times  in  succession.  The 
watchman  at  the  central  station,  being  thus  notified  of  the  existence 
and  locality  of  the  fire,  at  once  and  in  a  similar  manner  notifies  the 
several  fire-engine  companies. 


SECTION  XXX. 

USEFUL    APPLICATIONS    OF    ELECTRICITY    CONTINUED. 

557.  The  bolometer.  —  The  bolometer,1  also  called  a  thermic 
balance,  is  an  instrument  devised  by  Prof.  S.  P.  Langley  for 
measuring  minute  quantities  of  radiant  energy.  It  is  based 
upon  the  fact  that  when  equal  conductors  of  the  electrical 
current  are  at  the  same  temperature  their  conductivities  are 
equal,  and  the  current  of  a  battery  can  be  equally  divided 
between  them,  while,  if  unequally  heated,  their  conductivities 
are  unequal,  and  the  difference  can  be  detected  by  a  sensitive 
galvanometer.  By  the  substitution  of  thin  sheets  of  metal 
for  the  wires  ordinarily  used  as  conductors,  so  as  to  take  up 
and  part  with  radiations  with  great  rapidity,  an  instrument 
is  produced  capable  of  measuring  such  minute  changes  of 
temperature  as  a  hundred-thousandth  of  a  degree  centigrade. 

1  Bolometer,  ray -measurer. 


ALTERNATING   CURRENTS.  607 

It  has  achieved  results  of  immense  importance  in  astronom- 
ical and  optical  investigations,  especially  in  the  study  of  the 
distribution  of  heat  energy  in  the  solar  and  other  spectra. 
It  has  revealed  much  hitherto  unknown  concerning  the  infra- 
red region  of  the  spectrum.  It  has  demonstrated  that  the 
spectrum,  instead  of  being  confined  to  rather  less  than  an 
octave,  really  covers  far  more. 
To  JUAAXTVU  lA/l 

SECTION  XXXI. 

ALTERNATING    CURRENTS. 

558.  Tesla?s  investigations.1  —  Of  the  various  branches  of 
electrical  investigations  now  in  progress  perhaps  the  most 
interesting  and  most  promising  is  that-relating  to  alternating 
currents.  In  this  connection  a  few  words  concerning  the 
remarkable  experiments  of  Tesla  may  not  be  out  of  place. 

Tesla's  work  has  been  especially  with  alternating  currents 
of  very  high  frequency  and  enormously  high  potential.  In 
his  experiments  he  operates  an  induction  coil  either  with  a 
specially  constructed  alternating  dynamo  capable  of  giving 
many  thousands  of  reversals  of  current  per  second,  or  by  dis- 
ruptively  discharging  a  condenser  through  the  primary.  By 
the  latter  means  a  vibration  in  the  secondary  circuit  may  be 
produced  of  a  frequency  of  many  hundred  thousands  or  even 
millions  per  second.  The  discharge  produced  by  this  means 
is  quite  different  from  the  series  of  sparks  produced  by  the 
ordinary  induction  coil.  Herein  is  opened  to  the  experi- 
menter a  field  as  yet  quite  unexplored. 

If  two  straight  wires  terminate  the  secondary  coil  and  run 
parallel  to  each  other  for  a  short  distance,  the  discharge 
appears  in  the  form  of  powerful  brushes  and  luminous 

1  For  details  on  this  subject,  see  "  Experiments  with  Alternating  Currents  of 
High  Potential  and  High  Frequency"  by  Tesla. 


608  ETHER    DYNAMICS. 

streams  issuing  from  all  points  of  the  wires.  The  apparatus 
is  usually  enclosed  in  a  wooden  box  and  completely  immersed 
in  oil  that  the  insulation  may  be  more  nearly  perfect.  When 
an  ordinary  low  frequency  discharge  is  passed  through 
moderately  rarefied  air,  the  air  assumes  a  purplish  hue.  If 
by  some  means  the  intensity  of  the  molecular  or  atomic 
disturbance  be  increased,  the  gas  changes  to  a  white  color. 
A  similar  change  occurs  in  air  at  ordinary  pressure  when 
agitated  by  electric  impulses  of  very  high  frequency. 

The  chief  interest  in  investigations  along  this  line  seems 
to  lie  in  the  possibilities  they  offer  for  the  production  of  an 
efficient  illuminating  device.  The  present  means  of  produc- 
ing artificial  light  is  wofully  inefficient  and  wasteful.  Who 
can  say  that  it  is  not  to  be  by  means  of  alternating  currents 
of  high  frequency  and  high  potential  that  we  shall  soon  vie 
with  the  firefly  in  economical  illumination  ? 

Exercises. 

1.  (a)  Describe  and   explain  an  ordinary  multiplying  galvanoscope. 
(6)  Describe  a  coil  of  a  galvanoscope  suited  to  a  circuit  of  high  resistance, 
and  give  your  reason. 

2.  You  wish  to  make  of  an  iron  rod  an  electro-magnet  with  a  certain 
marked  end  as  an  N-pole.     Explain  the  method  by  a  diagram. 

3.  What  happens  to  a  fixed  bar  of  soft  iron  if  a  current  passes  above 
and  near  it  and  at  right  angles  to  it  ?     Make  a  diagram. 

4.  A  magnetic  needle  balanced  on  a  pivot  so  as  to  move  horizontally 
makes  11  vibrations  in  2  min.  1  sec.  at  a  place  A,  and  12  vibrations  in 
2  min.  at  a  place  B.     Compare  the  horizontal  components  of  the  earth's 
magnetic  force  at  A  and  B. 

5.  What  force  does  a  magnetic  pole,  the  strength  of  which  is  25  units, 
exert  upon  a  pole  the  strength  of  which  is  10  units  at  a  distance  of  10 
centimeters?  Ans.   2.5  dynes. 

6.  Upon  what  conditions  does  the  strength  of  the  current  furnished  by 
a  dynamo  depend  ? 

7.  If  a  current  be  sent   through  the  armature  of  a  dynamo,  what 
happens  ?     Why  ? 

8.  How  much  work  is  done  in  maintaining  a  current  of  10  amperes 
for  one  hour  in  a  circuit  against  a  resistance  of  50  ohms  ? 


EXEKCISES.  609 

9.  A  current  of  30  amperes  flows  through  a  wire.    What  heat  is  devel- 
oped in  an  hour  in  a  section  of  the  wire  whose  ends  differ  in  potential 
by  90  volts  ? 

10.  A  difference  of  potential  of  18.5  volts  is  maintained  at  the  ter- 
minals of  a  wire  of  .5  ohm  resistance.    What  is  the  activity  of  the  circuit 
in  joules  per  second  ?   -* 

11.  What  distinction  should  be  made  between  electricity  and  electrifi- 
cation ? 

12.  What  is  the  strength  of  a  current  which,  falling  15  volts,  yields 
.002  horse-power? 

13.  When  would  you  wind  an  electro-magnet  with  fine  wire  ? 

14.  Upon  what  does  the  E.M.F.  furnished  by  a  dynamo  depend  ? 

15.  A  dynamo  feeds  20  arc  lamps  in  series ;  the  average  resistance  of 
each,  including  the  lead  wires,  is  4.82  ohms.     The  dynamo  resistance  is 
8.2  ohms.     What  current  does  the  dynamo  furnish  with  an  E.M.F.  of 
560.4  volts  ? 

16.  A  current  of  10  amperes  deflects  the  needle  of  a  tangent  galvanom- 
eter 64°;  what  is  the  strength  of  a  current  which  will  deflect  the  same 
needle  70°  ? 

17.  Explain,  in  accordance  with  Ampere's  theory  of  magnetism,  the 
deflection  of  a  magnetic  needle  by  an  electric  current. 

18.  What  length  of  copper  wire  .012  in.  in  diameter  will  offer  a  resist- 
ance of  one  ohm  ? 

19.  How  many  coulombs  are  required  to  deposit  15  g  of  zinc  ? 

>  20.  In  what  time  will  a  current  of  one  ampere  decompose  10  g  of  water  ? 

21.  A  Daniell  battery  maintains  a  current  of  one  ampere  for  six  hours, 
(a)  What  quantity  of  zinc  will  be  consumed  ?     (6)  What  quantity  of 
copper  will  be  deposited  upon  the  negative  plate  of  each  cell  ? 

22.  In  an  electrolytic  cell,  4  grams  of  copper  were  deposited  in  one-half 
hour,     (a)  What  was  the  average  strength  of  current  ?     (6)  If  an  average 
difference  of  potential  of  3  volts  were  maintained  between  the  terminals 
of  the  cell,  what  would  be  the  average  activity  of  the  cell  ? 

23.  If  the  difference  of  potential  between  the  terminals  of  an  arc  lamp 
supplied  with  a  10-ampere  current  be  50  volts,  what  is  the  power  con- 
sumed in  the  lamp  ? 

24.  A  coil  of  platinum  wire  whose  resistance  is  4  ohms  is  submerged 
in  2  K  of  water  at  20°  C.  and  a  current  of  10  amperes  is  maintained  in 
the  coil.     In  what  time  will  the  temperature  of  the  water  be  raised  to 
100°  C.  (losses  by  radiation,  etc.  being  disregarded)  ? 

25.  (a)  Compare  the  activity  of  a  10-ampere  current  with  an  E.M.F. 
of  40  volts  with  the  activity  of  a  40  ampere  current  with  an  E.M.F.  of 


610  ETHEK    DYNAMICS. 

10  volts.  (6)  Suppose  that  these  currents  flow  through  wires  having  the 
same  resistance,  how  will  the  quantities  of  heat  developed  in  the  two  wires 
compare  ?  (c)  Suppose  that  it  is  desired  to  transmit  energy  to  a  great 
distance,  with  which  current  would  there  be  the  greater  waste  of  energy, 
provided  there  were  no  leakages  and  the  wires  were  of  the  same  kind, 
size,  and  length  ?  (d)  Which  current  would  be  the  most  difficult  to 
insulate  ?  (e)  With  which  current  is  a  greater  saving  in  the  cost  of 
conductors  possible  ? 

26.  A  Bunsen  cell  has  an  E.M.F.  of  1.9  volts  and  a  resistance  of  0.4 
ohm.     Its  plates  are  joined  first  by  a  2-ohm  wire,  second  by  a  28-ohm 
wire,     (a)  What  is  the  current  in  each  case  ?     (6)  What  quantity  of  heat 
is  generated  in  the  wire  in  each  case  ?     (c)  How  many  times  as  much 
heat  is  generated  in  one  case  as  in  the  other  ?     Why  ? 

27.  Two  hundred  incandescent  lamps  are  arranged  in  multiple  arc. 
Each  lamp  is  rated  at  110  volts  and  200  ohms,     (a)  What  is  the  resist- 
ance of  all  the  lamps  in  multiple  arc  ?     (6)  What  current  passes  through 
each  lamp  ?     What  horse-power  is  expended  on  their  lighting  ? 

28.  25  cells,  each  of  2  volts  and  1  ohm,  are  arranged  in  series  on  an 
external  circuit  of  250  ohms'  resistance.    The  efficiency  of  the  battery  (i.e. 
the  ratio  of  resistance  of  the  external  circuit  to  the  total  resistance  of  the 
circuit)  is  about  91  per  cent.     What  work  does  the  battery  do  in  that 
circuit  ? 

29.  A  battery  of  50  gravity  cells,  1  volt  3  ohms  each,  is  arranged  10  in 
multiple  arc  and  5  in  series.     What  is  the  resistance  and  E.M.F.  of  the 
battery  ? 

30.  A  battery  of  50  cells  arranged  to  give  80  volts  E.M.F.,  with  an 
internal  resistance  of  88  ohms,  sends  what  current  through  a  conductor 
of  100  ohms  resistance  ? 

31.  A  current  of  10  amperes  is  maintained  against  50  ohms'  resistance. 
What  is  the  electrical  horse-power  ? 

32.  An  electric  lamp  has  a  resistance  of  45  ohms;  it  is  connected  to  a 
street  main  by  leads  of  3  ohms  resistance.     What  portion  of  the  heat  is 
wasted  in  the  house  circuit  ? 

33.  Compare  the  quantities  of  heat  developed  in  a  100  volt  200  ohm 
lamp  and  in  a  35  volt  30  ohm  lamp. 

34.  A  difference  of  potential  of  5.5  volts  is  maintained  at  the  terminals 
of  a  wire  of  0.1  ohm  resistance,     (a)   What  current  flows  ?     (&)  What  is 
the  activity  of  the  circuit  in  joules  per  sec.  ? 


EXERCISES.  611 


REVIEW   EXERCISES. 

1.  Show  that  Newton's  First  Law  of  Motion  suggests  a  definition  of  force. 

2.  Explain  that  the  Second  Law  of  Motion  suggests  a  way  of  measuring 
forces. 

3.  Discuss  the  formula  ft  —  m  v. 

4.  A  force  of  80  dynes  acts  upon  a  mass  of  20  grams  for  10  seconds  ; 
what  velocity  does  it  produce  ? 

5.  A  constant  force  acting  upon  a  mass  of  25  g  causes  it  to  move  10 
meters  in  4  seconds  ;  what  is  the  magnitude  of  the  force  in  dynes  ? 

6.  How  long  must  a  force  of  5  dynes  act  upon  a  body  in  order  to  give 
it  a  momentum  of  3000  units  (the  unit  of  momentum  being  that  of  a  gram 
moving  at  the  rate  of  1  cm  per  sec.)  ? 

7.  Discuss  the  correctness  of  the  expression  "centrifugal  force." 

8.  Express  the  acceleration  due  to  gravity  in  our  latitude  in  meters 
per  minute. 

9.  A  force  of  10  Ibs.  acts  upon  a  mass  of  25  Ibs. ;  what  acceleration  is 
produced  ? 

10.  Find  the  value  of  g  at  a  place  where  the  seconds  pendulum  is 
0.994  m.  long. 

11.  Find  the  work  done  by  a  force  of  60  dynes  acting  through  a  dis- 
tance of  4  m. 

12.  A  stone  of  mass  8  K  falls  at  a  place  where  g  =  980.4  cm  per  sec. ; 
what  is  its  kinetic  energy  in  ergs  at  the  end  of  10  seconds  ? 

13.  What  should  be  the  horse-power  of  an  engine  intended  to  pump 
200   gallons   of    water   per  minute  to  a    hight  of  50  yds.?      (Assume 
1  gall.=c=101b.) 

14.  A  body  has  a  mass  of  1  K,  and  its  density  is  five  times  that  of 
water  ;  what  is  its  volume  ? 

15.  The  radii  of  two  spheres  are  2  cm  and  3  cm,  and  their  masses  are 
200  g  and  250  g  respectively  ;  compare  their  densities. 

16.  (a)  Find  the  pressure  in  dynes  per  cm2  caused  by  the  weight  of 
a  column  of  mercury  1  m  high.     (6)  In  grams  per  cm2. 

17.  Determine  the  available  water  pressure  (in  pounds  per  square 
inch)  in  a  laboratory  which  is  supplied  from  a  tank  at  a  hight  of  45  ft. 

18.  State  how,  with  a  mercury  manometer,  you  would  determine  the 
pressure  of  water  at  a  tap. 

19.  A  cube,  the  edge  of  which  is  one  decimeter,  is  suspended  in  water 
with  its  upper  surface  1  m  below  the  surface  of  the  water.    Find  the  pres- 
sure on  each  of  its  faces. 

20.  (a)   How  is  the  hight  of  the  mercurial  column  of  a  barometer 


614  ETHER    DYNAMICS. 

52.  An  object  is  placed  at  a  distance  of  10  cm  in  front  of  a  convex 
mirror  of  30  cm  focal  length  ;  where  will  the  image  be  formed  ? 

53.  A  candle-flame  1  in.  long  is  18  in.  in  front  of  a  concave  mirror 
whose  focal  length  is  15  in. ;  find  the  position  and  size  of  the  image. 

54.  The  relative  refractive  index  from  air  to  water  is  f ,  and  from  air 
to  glass  f  ;  find  the  relative  index  from  glass  to  water.  -» 

55.  If  an  object  at  a  distance  of  3  in.  from  a  convex  lens  has  its  image 
formed  on  the  opposite  side  of  the  lens  and  magnified  three  times,  what 
is  the  focal  length  of  the  lens  ? 

56.  Rays  of  light  diverging  from  a  point  8  in.  in  front  of  a  lens  are 
brought  to  a  focus  20  in.  behind  it ;  what  is  the  focal  length  of  the  lens  ? 

57.  A  person  whose  distance  of  most  distinct  vision  is  20  cm  uses  a 
lens  of  5  cm  focal  length  as  a  reading  glass ;  (a)  At  what  distance  from  a 
book  must  he  hold  it  ?     (6)  What  will  be  its  magnifying  power  ? 

58.  Two  small  spheres  are  at  a  distance  of  8  cm  apart ;   one  has  a 
charge  of  12  electrostatic  units,  the  other  of  8.     What  is  the  magnitude 
of  the  force  exerted  between  them  ? 

59.  Two  small  electrified  bodies  at  a  distance  of  12  cm  apart  are  found 
to  attract  each  other  with  a  force  of  6  units.     The  one  has  a  positive 
charge  of  32  electrostatic  units  ;  what  is  the  charge  of  the  other  ? 


60.  An  incandescent  lamp  takes  a  current  of  1.32  amperes,  and  the 
E.M.F.  between  its  terminals  is  66  volts;   what  is  its  resistance  when 
hot? 

61.  Copper  wire  T^  in.  in  diameter  has  a  resistance  of  8  ohms  per  mile; 
what  is  the  resistance  of  a  mile  of  copper  wire  JB  in.  in  diameter  ? 

62.  In  what  time  will  a  current  of  .5  ampere  deposit  8  g  of  silver  ? 

63.  What  is  the  strength  of  a  current  that  deposits  1  mg  of  zinc  per 
minute  ? 

64.  The  resistance  of  a  circuit,  including  that  of  the  battery,  is  18  ohms. 
What  change  will  be  produced  in  the  current  through  the  battery  if  two 
points  of  the  circuit,  between  which  the  resistance  is  12  ohms,  are  con- 
nected by  a  wire  of  4  ohms'  resistance  ? 

65.  What  shunt  is  required  to  reduce  to  one  one-hundredth  the  sen- 
sitiveness of  a  galvanometer  of  396  ohms'  resistance  ? 

66.  A  galvanometer  of  45  ohms'  resistance  is  shunted  by  a  resistance 
of  5  ohms.     Find  the  resistance  of  the  shunted  galvanometer  and  the 
current  which  flows  through  it  when  a  difference  of  potential  of  2  volts 
is  maintained  between  its  terminals. 


EXERCISES.  615 

67.  What  activity  in  horse-power  is  required  to  maintain  a  current  of 
4  amperes  through  a  resistance  of  37.3  ohms  ? 

68.  A  current  of  2  amperes  is  allowed  to  flow  for  half  an  hour  through 
a  coil  of  platinum  wire  of  6  ohms'  resistance  immersed  in  750  g  of  water. 
What  elevation  of  temperature  will  be  produced  by  it  ? 

69.  Find  the  efficiency  of  a  motor  from  the  following  tests  :  — 

E.M.F.  at  motor  terminals 125.2  volts. 

Current  in  external  circuit 100.9  amperes. 

Power  applied 18.62  h.  p. 

NOTE.  —  The  efficiency  of  a  motor  is  the  ratio  between  the  horse-power  developed 
by  the  motor  and  the  electrical  horse-power  absorbed  by  it. 

70.  The  resistance  of  an  incandescent  lamp  is  40  ohms,  and  the  dif- 
ference of  potential  between  its  two  terminals  is  45  volts.     Determine 
the  heat  produced  in  it  per  hour. 

71.  Ninety  incandescent  lamps  are  placed  in  multiple  arc,  and  a  current 
of  40  amperes  is  distributed  between  them,  the  E.M.F.  between  the  ter- 
minals being  120  volts.     The  resistance  of  the  conductors  is  .2  ohm,  and 
that  of  the  dynamo  .25  ohm,  and  the  insulation  resistance  between  the 
flow  and  return  conductors  is  1000  ohms.      What  horse-power  will  be 
required  for  electrical  work,  and  how  much  will  be  wasted  ? 


METRIC    UNITS. 

Inches 


Millimeters 


Centimeters 


Milliliter 


Cubic  Centimeter 


The  area  of  this  figure  is  a  square  decimeter. 
A  cube  of  water,  one  of  whose  sides  has  this 
area,  is  a  cubic  decimeter  or  a  liter  of  water, 
and  at  the  temperature  of  4°  C.  has  a  mass  of 
a  kilogram.  The  same  volume  of  air  at  0°  C., 
and  under  a  pressure  of  one  atmosphere,  has 
a  mass  of  1.293  grams.  The  grain  is  the  mass 
of  1  cc  of  pure  water  at  4°  C, 


Square    j 
Centimeter; 


Square  Inch 


100  Millimeters 


APPENDIX. 


TABLES  OP  METRIC  MEASURES. 


MEASURE  OF  LENGTH. 

1  Millimeter  (mm)  =  .001  meter  (m)  =  .03937  inch. 
1  Centimeter  (cm)  =  .01  meter  =  .39371  inch. 
1  Decimeter  (dm)  =  .1  meter  =  about  4  inches. 

1  Meter  =  39.37079  inches  =  about  3  ft.  3|  in. 
1  Dekameter  (Dm)  =  10  meters. 
1  Hektometer  (Hm)  =  100  meters. 
1  Kilometer   (Km)    =•  1000  meters  =  about  f  mile. 
1  Myriameter  (Mm)  =  10000  meters  =  about  6£  miles. 

MEASURE  OF  SURFACE. 

1  Square  millimeter  (mm2)  =  .000001  square  meter  (m2)  =  .0015  sq.  in. 

1  Square  centimeter  (cm2)  =  .0001  square  meter  =  .1550  sq.  in. 

1  Square  decimeter  (dm2)  =  .01  square  meter. 

1  Centare  =  1  square  meter  —  10.7643  sq.  ft.  =  about  li  sq.  yds. 

1  Are          =  100  square  meters. 

1  Hectare  =  10,000  square  meters  =  about  2-J-  acres. 

MEASURE  OF  VOLUME. 

1  Cubic  millimeter  (mm3)          =  .000000001  cubic  meter  (m3). 
1  Cubic  centimeter  (cm3  orcc)  =  .000001  m3  =  .061  cu.  in. 
1  Cubic  decimeter  (dm3)  =  .001  m3  =  1000  cm3. 

1  Cubic  meter  =  about  1.308  cu.  yds. 


618  APPENDIX. 


MEASURE  or  CAPACITY. 

1  Milliliter  (ml)  =  .001  liter  (1)  =  1  cc  =  .061  cu.  in. 
1  Centiliter  (cl)  =  .01    liter       =  10  cc. 
1  Deciliter          =  .  1      liter      =  100  cc. 

1  Liter         —  1000  cm2  =  61.027  cu.  in.  =  1.0567  qts. 
(liquid  measure). 


MEASURE  OF  MASS  AND  WEIGHT. 

1  Milligram  (mg)  =  .001  gram  (g)  =  .0154  grain. 
1  Centigram  (eg)  —  .01  gram  =  .1543  grain. 
1  Decigram  (dg)  =  .1  grain  =  1.5432  grains. 

1  gram  =  15.432  grains  —  .03527  av.  oz. 

1  Dekagram  (Dg)         =  10  grams. 
1  Hektogram  (Hg)        =  100  grams. 
1  Kilogram  (Kg  or  K)  =  1000  grams  =  2.2046  av.  Ibs. 
1  Myriagram  (Mg)       =  10,000  grams. 

1  cu.  ft.  of  water  at  62°  F.  has  a  mass  of  62.321  av.  Ibs.,  or  about  1000 
av.  oz.  1  cu.  in.  of  water  at  62°  F.  has  a  mass  of  .036  av.  Ib.  Pressure 
in  water  per  square  foot  increases  at  the  rate  of  about  62.3  Ibs.  for  every 
foot  of  depth,  or  per  sq.  in.  at  the  rate  of  about  £  Ib.  for  every  foot  of 
depth ;  or  per  cm2  at  the  rate  of  1  g  for  every  centimeter  of  depth,  or 
1  K  for  every  ten  meters  of  depth. 


TABLE  or  EQUIVALENT  VALUES. 

1  in.     =  .0254  m  -  2.53995  cm  =  about  2£  cm. 
1  ft.     =  .3048  m  =  30.48  cm      =  about  30|  cm. 
1  yd.    —  .9144  m  =  about  $$  m. 
1  mile  =  1609  m  =  about  1.609315  Km. 

1  sq.  in.  =  6.4514  cm2. 
1  sq.  ft.  =  929.01  cm2. 
1  sq.  yd.  =  8361.1  cm2  =  .83611  m2. 

1  cu.  in.   =  16.38618  cm3. 

1  cu.  ft.    =  28,316  cm8. 

1  cu.  yd.  =  764,526  cm3  =  about  .76m3. 


APPENDIX.  619 


1  U.  S.  pint    =  473  cm3. 

1  U.  S.  quart  =  946  cc  =  .946  1. 

1  U.  S.  gallon  (231  cu.  in.)  =  3784  cm3. 

1  gr.         =  .0647987  g. 

1  av.  oz.  =  28.3494  g. 

1  av.  Ib.  =  453.59  g  =  .45359  K  =  T5T  K. 


KEDUCTION  OF  MEASURES  TO  AND  FROM  THE  C.G.S.  SYSTEM. 

1  gram  weight    =  980  dynes  (where  g  =  980  cm  per  sec.). 

1  av.  Ib.  weight  =  4.445  X  105  dynes          "  " 

1  K  weight          =  980,000  dynes  ." 

1  Ib.  per  sq.  ft.  pressure  =  478.5          dynes  per  cm2. 

1  g  per  cm2  pressure         =  980  " 

1  atmosphere  (76  cm  0°)  =  1,012,630       " 

1  atmosphere  (30  in.  0°)  =  1,015,300       "          " 

1  gram-centimeter  =  980  ergs. 

1  erg  =  1  dyne-centimeter  =  .0000001  joule  =  ^  gram-centimeter. 

1  kilogrammeter  =  98,000,000  ergs  =  7.23314  ft.  Ibs. 

1  ft.  Ib.  =  13,550,000  ergs, 

1  foot-poundal     =  421,402  *  ergs. 

1  joule  =  10,000,000  *  ergs. 

33000  ft.  Ibs.  per  min.  =  about  7.452  X  109  ergs  per  sec. 


I  75  kilogram  meters  per  sec. =7. 35  X  109  ergs  per  sec. 
1  erg  per  sec.  =  .0000001  watt  or  volt-ampere. 

1  watt  —  1  joule  per  sec.  =  107  ergs  per  sec.  =  44.2394  ft.  Ibs.  per  mm. 
1  gram-degree  =  4.17  X  107  ergs. 
1  calorie  =  4.17  .X  10l°  ergs. 

1  Ib.  degree  F  =  1.051  X  1010  ergs  =  772  ft.  Ibs.  =  1047.03  joules. 

*  Independent  of  acceleration  of  gravity  (g). 


620 


APPENDIX. 


PROPERTIES  OF  SOLIDS. 


Specific 
Density 
17°. 

Hard- 
ness. 

Expan- 
sion 
Coefficient 
0°-100°. 

Melting 
Point. 

Specific 
Heat. 

Latent 
Heat  of 
Fusion. 

Refrac- 
tive 
Index. 

Agate 

2.6 
1.7 
2.7 
6.7 
5.7 
.8 
9.8 
.9 
8.3 
8.5 
1.7 
8.8 
1.07 
.7 

7 
2  + 
3 
3 
8 

2" 
3 

3  

.00002 
.00001 
.000007 

.000013 
.000019 

"700° 
432° 

266° 
900°? 

.21 
.05 

.08 

".03" 

"M 

.2  

".'09" 
.14 

1.54 

1.45 

Alum 

Aluminum  ,  
Antimony  .......I  
Arsenic  *1»  
Beech  
Bismuth  
Boxwood  
Brass  (cast)  
"      (hard  drawn) 
Bricks 

"is 

"L53 

2^47 
1.58 

L51 
1.62 

of 

1.66 
1.49 

Bronze  
Canada  Balsam  
Cherry 

"30 

"79!  7 
j  Ord. 
I  Extr. 

Copper 

8.8 
.24 
3.5 
2.7 
2.5 
8.5 
2.5 
3.6 
19.3 
2.7 
2.3 
.9 

2.7 

7.2 
7.7 
1.9 

3 

10 
8 
6 
3 

1.5 

6? 
4 

.000017 

1100° 

Cork  
Diamond 

Emerald  
Feldspar  
German-silver  
Glass  (crown)  
"     (flint)  
Gold 

".00002 
.000007 

.000012 

400° 
1050° 

o° 

1500° 

.19 
.03 

"".'20 
.5 

.11 

Granite  
Graphite  
Ice  

Iceland  spar  

Iron  (cast)  
"     (wrought)  
Ivory 

.000012 

1.53 

Lead  
Marble 

11.3 

2.7 
2.8 

2 
3 

.000028 

326° 

.03 
.21 

5 

Mica 

Paraffine  
Platinum  (wire)  
Quartz 

.9 
21.4 
2.6 
2.2 
2.3 
10.4 
2.8 
.9 
7.8 
2. 
2.6 
.9 
7.3 
7.1 

55° 
1800° 

"sob0 

'.03 
.21 

L54 
1.54 
1.52 

1.54 
•••—•• 

i"49 

7 
2 
2 

9?" 

i 

.000008 

Rock  sa.lt  O^Aq/rT 
Selenite  
Silver  
Slate  
Spermaceti  
Steel  (tempered)  
Sulphur  (native)  
Talc  
Tallow....,  
Tin  
Zinc  

.000019 
.000013 

1000° 
"440" 

115°' 

"40"o" 

232° 
360° 

.05 

""."bs" 

.17 

24 
9" 

2 
3 

.000019 
.00003 

.05 

.09 

14 

28 

APPENDIX. 


621 


PROPERTIES  OF  LIQUIDS. 


Specific 
Density. 

Coefficient 
Expan- 
sion at  0°. 

Freez- 
ing 
Point. 

Boiling 
Point 
760mm. 

Specific 
Heat. 

Refrac- 
tive 
Index. 

Acid,  nitric,  0°  
"      sulphuric,  0°...  L-.±.~ 
Alcohol  (grain),  0°.  £..  „..-... 
Benzine,  20°  
Carbon  dioxide,  20° 

1.5 

1.84 
.81 
.87 
1.37 

.00111 
.00059 
.00106 
.00118 

—  47° 
4° 

330°? 

78.2° 
80° 

.34 
.59 
.39 

1.43 
1.36 
1.49 

disulphide,  15°  
Ether,  0°  
Glycerine,  0° 

1.26 
.73 
1.26 

.00148 
.0005 

35° 
290° 

.23 
.54 

1.64 
1.35 
1.47 

Mercury,  0°  (Regnault) 

13  596 

00018 

—  39° 

350° 

034 

"         15°-20° 

13.558 

(solid)   -40°... 
Milk,  0° 

14.3 
1.032 

Oil  of  turpentine,  0°  
Olive  oil,  0°  

.89 
.92 

.00071 
.00080 

-10° 

160° 

.43 

1.47 
1.47 

Sea  water,  0° 

1.026 

Water,  0°                   OP 

.999 

oc 

100° 

1  00 

"       4.07®  

1.000 

1.33 

"       20° 

.998 

"       100°  

.958 

Air 

Ammonia 
Carbonic  acid 
Chlorine 


SPECIFIC  DENSITY  OF  GASES  AND  VAPORS. 
(Standard  :  Air  at  0°  C. ;  barometer,  76  cm.) 

1.0000   I   Hydrogen  ...H 0.0693 

0.5367    !   Nitrogen &L 0.9714 

1.5290      Oxygen (# 1.1057 

3.4400       Sulphuretted  hydrogen/^*  1-1912 

2.2474 


Hydrochloric  acid  .^^.£^.2540      Sulphurous  aci 


622 


APPENDIX. 


A  PORTION  OP  GLAISHER'S  HYGROMETRICAL  TABLES. 

Adapted  to  the  Use  of  the  Wet  and  Dry  Bulb  Thermometer. 


Reading 
of 
thermometer. 

Dew- 
point. 

Vapor 
pressure 
in  inches 
of 
mercury. 

Grains 
of  vapor 
in  1  cu.  ft. 
of  air. 

Grains 
required 
to 
saturate 
1  cu.  ft.  of 
air. 

Relative 
humidity. 

Mass  of 
1  cu.  ft. 
of  air 
in  grains, 
barom. 
reading 
29  in. 

Dry. 

Wet. 

Deg.  F. 

Degrees. 

Degrees. 

10 

10.0 

10.2 

0.068 

0.8 

0.0 

100 

573.1 

9.8 

8.2 

0.063 

0.8 

0.1 

92 

.2 

9.6 

6.5 

0.058 

0.7 

0.1 

85 

.2 

9.4 

4.7 

0.054 

0.7 

0.2 

78 

.2 

9.2 

3.0 

0.050 

0.6 

0.2 

72 

.3 

9.0 

1.2 

0.046 

0.6 

0.3 

67 

573.3 

11 

11.0 

11.0 

0.071 

0.9 

0.0 

100 

571.9 

10.8 

9.2 

0.065 

0.8 

0.1 

92 

572.0 

10.6 

7.5 

0.060 

0.8 

0.1 

85 

.0 

10.4 

5.7 

0.056 

0.7 

0.2 

78 

.0 

10.2 

4.0 

0.052 

0.7 

0.2 

72 

.1 

10.0 

2.2 

0.048 

0.6 

0.3 

67 

.1 

9.8 

0.5 

0.045 

0.6 

0.3 

62 

572.1 

12 

12.0 

12.0 

0.074 

0.9 

0.0 

100 

570.7 

11.8 

10.2 

0.068 

0.8 

0.1 

92 

.7 

11.6 

8.5 

0.063 

0.8- 

0.1 

85 

.7 

11.4 

6.7 

0.058 

0.7 

0.2 

78 

.8 

11.2 

5.0 

0.054 

0.7 

0.2 

72 

.8 

11.0 

3.2 

0.050 

0.6 

0.3 

66 

.8 

10.8 

1.5 

0.047 

0.6 

0.3 

61 

570.9 

13 

13.0 

13.0 

0.078 

1.0 

0.0 

100 

569.5 

12.8 

11.5 

0.072 

0.9 

0.1 

92 

.5 

12.6 

9.5 

0.066 

0.8 

0.2 

85 

.6 

12.4 

7.7 

0.061 

0.8 

0.2 

78 

.6 

12.2 

6.0 

0.056 

0.7 

0.3 

72 

.6 

12.0 

4.2 

0.052 

0.7 

0.3 

66 

.7 

11.8 

2.5 

0.048 

0.6 

0.4 

61 

.7 

11.6 

0.7 

0.045 

0.6 

0.4 

57 

569.7 

14 

14.0 

14.0 

0.082 

1.0 

0.0 

100 

568.2 

13.8 

12.2 

0.075 

0.9 

0.1 

92 

.3 

13.6 

10.5 

0.069 

0.9 

0.1 

85 

.3 

13.4 

8.7 

0.064 

0.8 

0.2 

78 

.3 

13.2 

7.0 

0.059 

0.7 

0.3 

72 

.4 

13.0 

5.2 

0.055 

0.7 

0.3 

66 

.4 

12.8 

3.5 

0.051 

0.6 

0.4 

61 

.4 

12.6 

1.7 

0.048 

0.6 

0.4 

57 

568.5 

APPENDIX.  623 


THE  C.G.S.  SYSTEM  OF  UNITS. 

The  C.G.S.  System  of  Units  is  the  result  of  an  attempt  to  express  all 
quantities  with  which  physical  science  deals  in  terms  of  three  funda- 
mental units  :  — 

A  Unit  of  Length,  the  centimeter ; 

A  Unit  of  Mass,  the  gram  ; 

A  Unit  of  Time,  the  second. 

From  these  the  following  units  are  derived  :  — 
Unit  of  Surface ;  the  square  centimeter. 

"     "   Volume ;  the  cubic  centimeter. 

"     "   Velocity;  the  velocity  of  one  centimeter  per  second. 

"  "  Acceleration;  the  acceleration  which  imparts  unit  velocity  to  a 
body,  in  one  second. 

"  "  Force;  the  dyne;  the  force  which,  acting  on  a  gram -mass  for 
one  second,  imparts  to  it  a  unit  of  velocity. 

"  "  Work;  the  erg  or  dyne-centimeter;  the  work  done  by  a  dyne 
working  through  one  centimeter. 

"  "  Energy ;  also  the  erg  ;  since  the  energy  of  a  body  is  measured  by 
the  amount  of  work  it  can  do. 

"  "  Heat;  the  calorie  (small),  amount  of  heat  required  to  raise  one 
gram  of  water  from  4°  to  5°  C. 

"  "  Magnetic  Strength;  a  magnetic  pole  has  unit  strength  when  it 
repels  a  similar  pole  of  equal  strength,  one  centimeter  dis- 
tant, with  the  force  of  a  dyne. 

"  "  Electric  Current  (electro-magnetic  system);  a  current  of  such 
strength  that  one  centimeter  of  its  circuit,  bent  so  that  every 
point  of  it  is  one  centimeter  distant  from  a  unit  magnetic 
pole,  exerts  upon  this  pole  the  force  of  a  dyne. 

"  "  Electric  Quantity  (electro-magnetic  system) ;  the  quantity  con- 
veyed by  a  unit  current  in  one  second. 

"     "  Difference  of  Potential   (electro-magnetic   system)  ;    two  points 
have  a  unit  difference  of  potential  when  one  erg  of  work 
must  be  expended  to  bring  a  unit  of  +  electricity  from  one 
.     to  the  other  against  the  electric  force. 

"  "  Electric  Resistance  (electro-magnetic  system) ;  a  conductor  pos- 
sesses unit  resistance  when  a  unit  difference  of  potential 
between  its  ends  causes  a  unit  current  to  flow  through  it. 


624  APPENDIX. 


ALPHABETICAL  TABLE  OF  UNITS  USED  IN 
PHYSICAL  SCIENCE. 

Activity.     See  Force-de-cheval,  Horse-power,  and  Watt. 
Ampere  ;  unit  of  electric  current ;  10— l  C.G.S.  units ;  the  current  pro- 
duced by  the  difference  of  potential  of  a  volt  through  the  resistance 

of  an  ohm. 
Calorie  ;  unit  of  heat ;  quantity  of  heat  required  to  raise  one  kilogram 

of  water  from  4°  to  5°  C.  equals  3.968  Eng.  units  of  heat.     (See  Heat, 

English  unit  of.) 
Capacity.     See  Farad. 
Coulomb;  unit  of  quantity  of  electricity;  10— x  C.G.S.  units;  quantity 

conveyed  by  a  current  of  one  ampere  in  a  second. 
Current.     See  Ampere. 
Dyne  ;  C.G.S.  absolute  unit  of  force. 
Electro-motive  force.     See  Volt. 
Erg  ;  C.G.S.  absolute  unit  of  work  or  energy. 
Farad;  unit  of  electric  capacity;   10— 9  C.G.S.  units;  the  capacity  of 

a  condenser  which  can  be  charged  to  a  potential  of  one  volt  by  one 

coulomb. 
Foot-pound ;  English  unit  of  work ;  work  required  to  raise  one  pound 

through  one  foot  in  opposition  to  the  force  of  gravity. 
Foot-poundal ;  F.P.S.  absolute  unit  of  work  or  energy  ;  the  work  done 

or  energy  imparted  by  one  pound  working  through  one  foot. 
Force.     See  Dyne,  Kilogram  and  Pound. 
Force-de-cheval ;  French  unit  of  activity  ;  0.9864  horse-power  ;  capacity 

for  doing  75  kilogrammeters  (542.5  foot-pounds)  of  work  per  second. 
Gram-centimeter  ;  gravitation  unit  of  work  or  energy  =C=  9  ergs. 
Heat,  English  unit  of  ;  heat  required  to  raise  one  pound  of  water  from 

32°  to  33°  F.     (See  Calorie.) 
Horse-power  ;  English  unit  of  activity  ;  activity  required  to  perform  550 

foot-pounds  of  work  per  second. 
Joule  ;  107   ergs ;  electrical  unit  of  work.     It  is  the  work  done  in  one 

second  when  the  rate  of  working  is  one  watt :  in  other  words,  that 

done  in  one  second  in  maintaining  a  current  of  one  ampere  against 

a  resistance  of  one  ohm. 

Kilogram  ;  metric  unit  of  mass,  and  also  of  force.     (See  Pound.) 
Kilogrammeter  ;  French  unit  of  work  ;  work  required  to  raise  one  kilo- 
gram of  mass  through  one  meter  in  opposition  to  the  force  of  gravity. 


APPENDIX.  625 

Mass.     See  Kilogram  and  Pound. 

Ohm;   unit  of  electric  resistance;    109  C.G.S.  units;  see  International 

Ohm,  p.  489. 
Potential.     See  Volt. 
Pound  ;  English  unit  of  mass  ;  regarded  as  a  weight  it  is  used  also  as  the 

unit  of  force,  i.e.  the  force  exercised  on  the  mass  of  a  pound  by 

gravitation  (where  g  —  981 ;  London). 
Quantity.     See  Coulomb. 
Resistance.     See  Ohm. 
Volt;  unit  of  electro-motive  force;  108  C.G.S.  units:    equals  .9268  of 

the  E.M.F.  of  one  Daniell  cell. 
Watt ;  unit  of  electric  activity  ;  107  ergs  per  second  ;  activity  exerted  by 

a  current  of  one  ampere  against  a  difference  of  potential  of  a  volt. 
Watt-hour  ;  electrical  unit  of  work  =0=  3600  joules. 
Work.     See  Foot-pound,  Kilogrammeter,   Gram-centimeter,  Erg,  Joule, 

and  Watt-hour. 


TABLE  OF  KESISTANCE  OF  WIKE, 

Chemically  pure,  one  meter  long,  one  millimeter  in  diameter, 
at  0°  C.  (Jenkin).     Also  relative  resistances  (Ayrton). 


Silver,  annealed  .  . 

.03937  ohm 

Relative 
Resistances. 

1  000 

"  hard  drawn  
Copper,  '  ' 

02103    " 
02104    " 

1.086 
1  086 

Zinc,  pressed  
Platinum  
Iron,  annealed  
Lead,  pressed 

.07244    " 
.11660    " 

12510    "     .. 
25270    " 

3.741 
6.022 
6.460 
13  050 

German-silver  ... 

.26950    " 

13.920 

626 


APPENDIX. 


VALUES  OF  PRACTICAL  ELECTRICAL  UNITS  IN  C.G.S.  ELECTRO- 
MAGNETIC UNITS. 

Electro-motive  force Volt  =  108. 

Kesistance  ...: Ohm  —  109. 

Current Ampere  =  10-1. 

Quantity Coulomb  =  10-1. 

Capacity ..  Farad  =  10~9. 


TABLE  or  TRIGONOMETRICAL  FUNCTIONS. 


Degree. 

Tangent. 

Sine. 

Degree. 

Tangent. 

Sine. 

Degree. 

Tangent. 

Sine. 

1 

.017 

.017 

31 

.601 

.515 

61 

* 
1.80 

.875 

2 

.035 

.035 

32 

.625 

.530 

62 

1.88 

.883 

3 

.052 

.052 

33 

.649 

.545 

63 

1.96 

.891 

4 

.070 

.070 

34 

.675 

.559 

64 

2.05 

.899 

5 

.087 

.087 

35 

.700 

.574 

65 

2.14 

.906 

6 

.105 

.105 

36 

.727 

.588 

66 

2.25 

.914 

7 

.123 

.122 

37 

.754 

.602 

67 

2.36 

.921 

8 

.141 

.139 

38 

.781 

.616 

68 

2.48 

.927 

9 

.158 

.156 

39 

.810 

.629 

69 

2.61 

.934 

10 

.176 

.174 

40 

.839 

.643 

70 

2.75 

.940 

11 

.194 

.191 

41 

.869 

.656 

71 

2.90 

.946 

12 

.213 

.208 

42 

.900 

.669 

72 

3.08 

.951 

13 

.231 

.225 

43 

.933 

.682 

73 

3.27 

.956 

14 

.249 

.242 

44 

.966 

.695 

74 

3.49 

.961 

15 

.268 

.259 

45 

1.000 

.707 

75 

3.73 

.966 

16 

.287 

.276 

46 

1.036 

.719 

76 

4.01 

.970 

17 

.306 

.292 

47 

1.07 

.731 

77 

4.33 

.974 

18 

.325 

.309 

48 

1.11 

.743 

78 

4.70 

.978 

19 

.344 

.326 

49 

1.15 

.755 

79 

5.14 

.982 

20 

.364 

.342 

50 

1.19 

.766 

80 

5.67 

.985 

21 

.384 

.358 

51 

1.23 

.777 

81 

6.31 

.988 

22 

.404 

.374 

52 

1.28 

.788 

82 

7.12 

.990 

23 

.424 

.390 

53 

1.33 

.799 

83 

8.14 

.993 

24 

.445 

.407 

54 

1.38 

.809 

84 

9.51 

.995 

25 

.466 

.423 

55 

1.43 

.819 

85 

11.43 

.996 

26 

.488 

.438 

56 

1.48 

.829 

86 

14.30 

.998 

27 

.510 

.454 

57 

1.54 

.839 

87 

19.08 

.999 

28 

.632 

.469 

58 

1.60 

.848 

88 

28.64 

.999 

29 

.554 

.485 

59 

1.66 

.857 

89 

57.29 

1.000 

30 

.577 

.500 

60 

1.73 

.866 

90 

Infinite 

1.000 

INDEX. 


[Numbers  refer  to  pages.] 


Aberration,  Chromatic,  371 ;  Spheri- 
cal, of  lenses,  366,  of  mirrors,  340. 

Absolute  units,  4;  zero,  273;  tem- 
perature, 274. 

Absorbers  of  radiation,  422. 

Acceleration  defined,  9;  Rate  of,  9. 

Accumulators,  579. 

Action  and  reaction,  35,  68. 

Activity  denned,  95  ;  of  an  electric 
current,  492 ;  Transmission  of 
electrical,  581 ;  Units  of,  96. 

Adheshn,  33. 

Air-pump,  168 ;  Mercury,  169. 

Alphabetical  table  of  physical  units, 
624. 

Alternating  currents,  607. 

Amalgamating  zincs,  408. 

Ammeter,  498. 

Ampere,  486. 

Amperian  currents,  545. 

Ampere-hour,  494. 

Ampere"1  s  laws  of  currents,  542  ; 
theory  of  magnetism,  543. 

Ampere-volt,  see  Watt. 

Armature,  483 ;  Classes  of,  570 ; 
Gramme,  564  ;  Siemen's,  564. 

Artesian  wells,  152. 

Astigmatism,  432. 

Athermancy,  416. 


Atmospheric    pressure,    155  ;    how 

measured,  157. 
Atomic  theory,  126. 
Atoms,  126. 
Aurora,  461. 

Axes,  Secondary,  341,  359. 
Axis,  Optic,  403. 


Barometer,  158  ;  aneroid,  160  ;  For- 
tin,  159 ;  in  meteorology,  162 ; 
for  measuring  bights,  161. 

Battery,  E.M.F.  of,  519;  of  high 
E.M.F.,  519;  of  low  resistance, 
511  ;  Storage,  579 ;  Theory  of, 
467  ;  Thermo-electric,  584  ;  Vol- 
taic, 510. 

Beam  of  light,  320. 

Beats  in  music,  222. 

Body  of  matter  defined,  4. 

Boiling  point,  281. 

Bolometer,  606. 

Boyle's  law,  164. 

Buoyant  force  of  fluids,  175. 


Calorescence,  386. 

Calorie,  260;  small,  261. 

Calorimetry,  260. 

Camera,  Photographer's,  429. 


628 


INDEX. 


Candle-power,  327. 

Capacity,  Electrical,  451;  Heat, 
261 ;  Inductive,  446. 

Capillarity,  133. 

Carcel,  327. 

Cells,  Best  arrangement  of,  512 ; 
Methods  of  combining,  510;  Vol- 
taic, 470-3. 

Center  of  mass,  8,  53;  how  to  find, 
55. 

Center  of  oscillation,  80;  of  per- 
cussion, 81. 

Central  force,  72;  magnitude  of ,  73. 

Centrifugal  tendency,  73. 

Centroid,  8,  53. 

Circuit,  Electric,  466;  Ground,  466. 

Cohesion,  129  ;  of  liquids,  133. 

Cold,  Method  of  producing  arti- 
ficially, 288. 

Collimator,  375. 

Color,  by  absorption,  386  ;  Cause 
of,  372. 

Colors,  Complementary,  393  ;  Mix- 
ing, 389 ;  of  thin  plates,  397. 

Commutator,  562. 

Composition  of  forces  defined,  46 ; 
of  forces  acting  at  angles,  58  ;  of 
forces  acting  in  the  same  line, 
45 ;  of  parallel  forces,  48,  49  ;  of 
velocities,  16,  18. 

Condenser,  Capacity  of  electrical, 
456 ;  Electrical,  455. 

Conduction,  Electrolytic,  468;  of 
heat,  294. 

Contact  action,  459. 

Contrast,  Effects  of,  394. 

Convection  of  heat,  296. 

Coulomb,  486. 

Coulomb-meter,  494. 

Couple,  Dynamical,  50;  Moment 
of  a,  51. 


Critical  angle,  353. 

Current  detector,  481;  Magnetic, 
537;  Strength  of,  485. 

Currents,  Attraction  and  repulsion 
between,  541;  Eddy,  563;  Extra, 
553 ;  Thermo-electric,  582. 


Declination,  Angle  of,  532. 

Density,  111 ;  Electric,  447  ;  For- 
mulas for,  178;  Specific,  177. 

Densimeter,  180. 

Dew,  422. 

Dew-point,  291. 

Diathermancy,  416. 

Dielectric,  440 ;  Condition  of,  457. 

Diffraction,  395,  398 ;  grating,  398. 

Diffusion  of  liquids,  138;  of  gases, 
139. 

Discord,  223. 

Dispersion,  Cause  of  color,  372. 

Distillation,  287. 

Divided  circuits,  508;  Kirchhoff's 
law  of,  509.  ' 

Ductility,  133. 

Dyalisis,  140. 

Dynamics  defined,  33. 

Dynamo,  Action  of,  560;  Alternat- 
ing current,  562  ;  defined,  557  ; 
Direct-current,  563;  Edison,  569  ; 
Principle  of,  557;  Reversibility 
of,  571 ;  Weston,  568. 

Dynamometer,  42. 

Dynamos,  Classes  of,  566. 

Dyne,  40. 


Ear,  242. 

Earth  a  magnet,  530. 
Earth's  rotation,  Demonstration  of, 
82. 


INDEX. 


629 


Eddy  currents,  564. 

Effects  of  points  on  electric  charges, 
448;  produced  by  electric  cur- 
rent, 474. 

Elasticity,  130 ;  of  gases,  166. 

Electric  attraction  and  repulsion  re- 
garded as  ether  strain,  436 ;  Law 
of,  437. 

Electric  conduction,  439 ;  density, 
447  ;  induction,  442 ;  lamp,  589 ; 
machines,  452  ;  motor,  573 ;  rail- 
ways, 581. 

Electric  current,  Rules  relating  to, 
492. 

Electricity  acts  across  a  dielectric, 
441;  What  is  ?  436  ;  Quantity  of, 
437. 

Electrification,  434 ;  Two  kinds  of, 
435. 

Electro-chemical  series,  465. 

Electrokinetics,  462. 

Electroscope,  438,  463. 

Electrolysis,  475 ;  Reversibility  of, 
579. 

Electrolyte,  464. 

Electro-magnets,  482. 

Electro-magnetic  units,  485. 

Electro-motive  force,  486. 

Electrophorus,  452. 

Electroplating,  594. 

Electrostatics,  449. 

Electrostatic  units,  491. 

Electrotyping,  593. 

Energy,  Absolute  units  of,  89 ;  Cal- 
culating, 90,  91 ;  contrasted  with 
momentum,  92  ;  Definition  of, 
84 ;  Dissipation  of,  250  ;  Doc- 
trines of  correlation  and  conser- 
vation of,  303 ;  Gravitation  units 
of,  88  ;  Kinetic,  85  ;  Potential, 
86;  The  sun  a  source  of,  250. 


Engines,  Steam,  310. 

Equilibrium  of  forces,  46 ;  of  mo- 
ments, 50;  Three  states  of,  55, 
561. 

Equilibrant,  46. 

Equipotential  surfaces,  526. 

Erg,  89. 

Ether,  The,  315. 

Evaporation,  281;  Kinetic  theory 
of,  281. 

Expansion,  Anomalous,  270 ;  by 
heat,  265;  coefficients,  228;  Force 
exerted  in,  269. 

Expansive  force  of  gases,  272. 

Extra  currents,  553. 

Eye,  429. 


Faradaifs  ice-pail  experiment,  445. 

Fire-alarm,  605. 

Field  of  force,  459. 

Fluid,  Perfect,  131. 

Fluids,  128  ;  Pressure  of,  147. 

Fluorescence,  385. 

Foci,  Conjugate,  339,  361. 

Focus,  338;  Principal,  339;  Vir- 
tual, 361. 

Force,  Absolute  units  of,  40  ;  Cen- 
tral, 72;  Centrifugal,  73;  defined, 
34  ;  Graphical  representation  of, 
45 ;  Gravitation  units  of,  41  ; 
Measurement  of,  40,  42,  43  ; 
Moment  of,  50  ;  Two  systems  for 
measuring,  43  ;  Unbalanced,  46. 

Forces,  Composition  of,  46  ;  Com- 
position of  angular,  58 ;  Paral- 
lel, 48,  49  ;  Equilibrium  of,  46  ; 
Polygon  of,  61  ;  Resolution  of, 
46,  62  ;  Triangle  of,  61. 

Fraunhofer's  lines,  380. 

Fusion,  276  ;  Heat  of,  278. 


630 


INDEX. 


Galvanometer,  495  ;  constant,  498  ; 
Reduction  factor  of,  498  ;  Tan- 
gent, 497  ;  Thomson's  mirror, 
495;  Shunted,  510;  Standard- 
izing of,  498. 

Galvanoscope,  481. 

Gaseous  bodies,  Laws  of,  274. 

Gratings,  Diffraction,  398  ;  Reflec- 
tion, 401. 

Gravitation,  39  ;  Determination  of 
force  of,  79  ;  Law  of  Universal, 
119  ;  Variation  of,  120,  121. 


Harmony  and  discord,  223. 

Hardness,  132. 

Heat,  Capacity  for,  261  ;  Capacity 
of  water  for,  264  ;  Conduction  of, 
294 ;  consumed  in  dissolving  and 
evaporating,  298  ;  Convection  of 
296,  302 ;  Convertible  into  mass 
energy,  246  ;  Diffusion  of,  294  ; 
Mechanical  equivalent  of,  307  ; 
Origin  of  animal,  249  ;  Sources 
of,  248 ;  Specific,  261  ;  Theory 
of,  247. 

Heat  energy  transformed  into  me- 
chanical energy,  582. 

Hertz's  researches,  586. 

Humidity,  Relative,  293. 

Hydraulic  press,  146. 

Hydrokinetics,  142. 

Hydrostatic  transmission  of  pres- 
sure, 142. 

Hydrostatics,  142. 

Hypermetropia,  432. 


Illumination,  Intensity  of,  327. 
Images,  by  apertures,  322  ;  by  con- 


cave mirrors,  340  ;  by  converg- 
ing lenses,  362  ;  of  images,  336  ; 
Real,  341  ;  Reversion  of,  336  ; 
Virtual,  335,  365. 

Incandescent  lamps,  590. 

Inclination,  Angle  of,  534. 

Induction  coils,  555 ;  Electric,  442 ; 
Electro-magnetic,  546  ;  Electro- 
static, 446,  452  ;  Faraday's  law 
of,  550 ;  Lenz's  law  of,  552  ;  Mag- 
netic, 521,  530;  Self,  553. 

Inductive  capacity,  446. 

Inertia,  65  ;  Quasi-electrical,  554. 

Insulation,  440. 

Interference  of  sound-waves,  214, 
239  ;  Young's  theory  of,  395. 

Irrationality  of  dispersion,  400. 

Isogonic  curves,  533. 


Joule,  488. 

Joule's    equivalent,    307  ;     experi- 
ment, 304. 

K 

Kinematics,  6. 

Kinetic  energy,  85  ;  theory  of  mat- 
ter, 270. 
Kinetics,  46. 


Lamps,  Arc,  589 ;  Incandescent, 
590. 

Law  of  sines,  Snell's,  351  ;  Boyle's 
164. 

Laws,  Physical,  5. 

Lenses,  358  ;  Achromatic,  372 ; 
Aplanatic,  3(57  ;  Diverging,  362, 
366  ;  Effect  of,  359  ;  Law  of  con- 
verging, 361. 

Lenz's  law  of  induction,  552. 


INDEX. 


631 


Ley  den  jar,  456. 

Light,  318  ;  Diffused,  333 ;  Electric, 
587  ;  Intensity  of  reflected,  333  ; 
Maxwell's  theory  of,  585 ;  Pris- 
matic analysis  of,  368  ;  Speed  of, 
325  ;  Synthesis  of  white,  370. 

Lightning,  460. 

Lightning  rods,  460. 

Line  of  direction,  54. 

Lines  of  force,  549 ;  Magnetic,  478, 
523,  525,  529. 

Locomotive,  312. 

Luminous  objects,  319. 

M 

Machines,  98  ;  Efficiency  of,  101 ; 
Electrical,  452 ;  Universal  law 
of,  101. 

Magnets,  forms  of,  522;  Law  of,  520. 

Magnetic  attraction  and  repulsion, 
526  ;  current,  537;  equator,  535  ; 
field,  478,  528,  529,  536  ;  poles 
of  the  earth,  531 ;  storms,  536  ; 
transparency,  521. 

Magnetic  force,  Lines  of,  478. 

Magnetic  needle,  Deflection  of,  479. 

Magnetism,  Ampere's  theory  of, 
543. 

Malleability,  133. 

Manometer,  166. 

Manometric  flames,  228. 

Mass,  2  ;  Center  of,  53. 

Matter,  4  ;  Critical  state  of,  128  ; 
Kinetic  theory  of,  270  ;  Minute- 
ness of  particles  of,  125  ;  Theory 
of  constitution  of,  125 ;  Three 
states  of,  127;  Ultragaseous  state 
of,  129. 

Microscope,  Compound,  424  ;  Mag- 
nifying power  of,  426  ;  Simple, 
365. 


Mechanical  powers,  102. 

Mirrors,  331. 

Molar  force,  129. 

Molecule,  124. 

Molecular  forces,  129. 

Moment  of  a  couple,  51 ;  of  a  force, 
50. 

Momentum,  36,  37. 

Moments,  Equilibrium  of,  50. 

Monochromatic  light,  372. 

Motion,  5;  Absolute,  7;  Compo- 
sition of  circular,  25;  Curvilinear, 
how  produced,  72 ;  Graphical 
representation  of,  16  ;  Laws  of 
uniformly  accelerated,  11 ;  New- 
ton's laws  of,  65-70  ;  of  transla- 
tion and  rotation,  22  ;  Rectilinear 
and  curvilinear,  24  ;  Relative,  7 ; 
Simple  Harmonic,  25. 

Musical  instruments,  254. 

Musical  scale,  211  ;  Limits  of,  212. 

Musical  sound  versus  noise,  210. 

Mutual  action  of  currents,  540. 

Myopia,  431. 

N 

Nevitori's  rings,  397. 
Nicol  prisms,  404. 
Nodes,  219. 


Oculars,  426. 

Ohm,  488. 

Ohm's  law,  490;  Verification  of,  517. 

Opalescence,  388. 

Oscillation,  Center  of,  80. 

Osmose  of  fluids,  140. 


Parallelogram    of    forces,   60 ;    of 
velocities,  18. 


632 


INDEX. 


Pascal's  principle,  147. 

Pencil  of  light,  320. 

Pendulum,  simple  and  compound, 
80. 

Penumbra,  323. 

Percussion,  Center  of,  81. 

Phenomenon,  5. 

Phonautograph,  231. 

Phosphorescence,  385. 

Photometer,  328. 

Photometry,  328. 

Photophone,  604. 

Physics,  33. 

Pigments,  Mixing,  391. 

Pitch  of  musical  sounds,  207. 

Plasticity,  130. 

Pneumatics,  142. 

Polariscopes,  407,  412. 

Polarity,  521. 

Polarization  by  double  refraction, 
404,  409  ;  by  reflection,  408  ; 
Chromatic  phenomena  of,  410  ; 
Circular  and  elliptical,  410;  Plane 
of,  407  ;  of  negative  plate,  469 ; 
Rotatory,  414. 

Porosity,  125. 

Potential,  449. 

Potential,  Difference  of,  517  ;  Mag- 
netic, 529. 

Power,  see  activity. 

Presbyopia,  432. 

Pressure,  47 ;  of  fluids,  147;  of  gases 
due  to  kinetic  energy  of  mole- 
cules, 271. 

PrevosVs  theory  of  exchanges, 
421. 

Prisms,  Nicol,  404  ;  Optical,  357. 

Pump,  Air,  168 ;  Force,  174  ;  Lift- 
ing, 173. 

Pyrheliometer,  420. 

Pyrometers,  259. 


Quality  of  sound,  226. 
Quantity,  1. 


Radiant  energy,  316 ;  Effects  of, 
317. 

Radiation,  303,316;  Heat  not  trans- 
mitted by,  416;  Only  one  kind  of, 
384;  Solar,  420. 

Radiators,  317;  Good,  422. 

Radiometer,  419. 

Radiophone,  604. 

Ray  of  light,  320 ;  Extraordinary, 
403 ;  Ordinary,  402. 

Reflection,  Doubled  angle  of,  332 ; 
from  concave  mirrors,  338  ;  grat- 
ings, 401  ;  Law  of,  331 ;  Total, 
353. 

Refraction,  346 ;  Cause  of,  347  ; 
Double,  402  ;  Failure  of  emission 
theory  to  account  for,  349 ;  Index 
of,  350 ;  Measurement  of  index 
of,  357. 

Revelation,  277. 

Relation  of  energy  to  force  and 
matter,  87. 

Relay  and  repeater,  Telegraph, 
597. 

Resistance,  Electrical,  488,  500 ; 
Measurement  of,  503-507. 

Resolution  of  forces,  62 ;  of  veloci- 
ties, 19. 

Resultant  force,  46. 

Retentimty,  Magnetic,  521. 

Reversibility  of  the  dynamo,  571. 

Rigidity,  130. 

Ring  system  of  plates,  412. 

Rotation  of  magnet  about  a  current, 
and  vice  versa,  544. 

Ruhmkorff's  coil,  556. 


INDEX. 


633 


Saccharimeter,  415. 

Shadows,  323. 

Siphon,  170. 

Solar  and  stellar  chemistry  and 
physics,  382. 

Solenoid,  538. 

Sonometer,  218. 

Sound,  How  it  originates,  186 ; 
Quality  of,  226. 

Sounder,  Telegraph,  597. 

Sound-waves,  Analysis  of,  227  ;  En- 
ergy of,  194  ;  how  propagated, 
187;  Interference  of,  214;  Na- 
ture of,  191  ;  Reenforcement  of, 
201  ;  Reflection  of,  197  ;  Refrac- 
tion of,  199;  Speed  of,  192,  203; 
Synthesis  of,  233. 

Spectroscopes,  374  ;  Direct  vision, 
376. 

Spectrum  analysis,  378 ;  Normal, 
400. 

Spectrums,  Bright  line,  376  ;  Con- 
tinuous, 374  ;  Distribution  of  en- 
ergy in,  383 ;  Reversed,  dark 
line,  or  absorption,  378. 

Specific  density,  177  ;  heat,  261  ; 
heat  of  gases,  265. 

Speed  of  light,  325 ;  of  sound- 
waves, 192,  203. 

Spherical  aberration  of  lenses,  366  ; 
of  mirrors,  340. 

Spheroidal  state,  290. 

Statics,  46. 

Stability  of  bodies,  56. 

Steam-engine,  308  ;   Power  of,  313. 

Stereopticon,  432. 

Storage  batteries,  579. 

Strain,  130. 

Strength,  Tensile,  47,  130. 

Stress,  69. 


Substance,  5. 
Suction,  167. 
Surface  tension,  134. 


Table,  Alphabetical,  of  physical 
units,  624  ;  of  electrical  resist- 
ances, 625 ;  of  natural  tangents, 
626. 

Tables,  Hygrometrical,  622 ;  of 
metric  measures,  617  ;  of  specific 
density,  etc.,  620. 

Telegraph,  595. 

Telephone,  599. 

Telescope,.  427  ;  Newtonian  reflect- 
ing, 428; 

Temperature,  251  ;  Absolute,  274  ; 
Thermo-dynamic  definition  of, 
274. 

Tenacity,  129. 

Tension,  47  ;  Surface,  134. 

Testa's  investigations,  607. 

Thermometers,  Construction  and 
graduation  of,  254 ;  Standard, 
259  ;  Self-registering,  257  ;  Wet 
and  dry  bulb,  293. 

Thermometry,  253. 

Thermo-dynamics,  303 ;  Laws  of, 
306. 

Thermo-electric  currents,  582. 

Thermo-multiplier,  584. 

Tones,  221. 

Tb'pler-Holtz  electrical  machine, 
452. 

Trade-winds,  297. 

Transformation  of  heat  reversible, 
280. 

Transformer,  575. 

Translucency,  321. 

Transparency,  321 ;  magnetic,  52 1. 

Tubes  of  force,  257. 


634 


INDEX. 


Undulatory  theory  of  light,  319. 
Unit  of  mass,  2  ;  of  length,  2  ;  of 

time,  4. 
Units,   Absolute,   4 ;    Derived,    4  ; 

Fundamental,    1 ;    Gravitation, 

39,  90  ;  Thermal,  260. 


Vacuum,  Torricellian,  159. 
Vaporization,  281  ;  Heat  of,  285. 
Variation  of  the  magnetic  needle, 

532. 
Velocity,  8  ;  Angular,  23 ;  Constant 

and  accelerated,  8. 
Velocities,  Composition  of,  16. 
Ventilation,  298. 
Vibrations,  Complex,  220  ;  Forced 


and  sympathetic,  205  ;   Station- 
ary, 219. 

Viscosity,  131. 

Vision,  Defects  of,  431  ;  Young's 
theory  of  color,  392. 

Visual  angle,  330. 

Vocal  organs,  240. 

Volt,  487. 

Voltaic  cells,  465. 

Voltameter,  494. 

Volume,  4. 

W 

Watt,  488,  492. 

Wave-motions,  31. 

Weight,  39  ;  Variation  of,  121. 

Wheatstone  bridge,  504. 

Work,  84  ;  Calculating,  90  ;  Elec- 
trical, 488  ;  Formulas  for  calcu- 
lating, 90  ;  Units  of,  88,  89. 


ADVERTISEMENTS 


Chain    and    Sprocket    Problem. 

To  the  Editor  of  the  SCIENTIFIC  AMERICAN  : 

As  the  theory  of  the  movement  of  a  bicycle  is  being 
gradually  introduced  into  text  books  on  mechanics  and 
discussed  in  mathematical  journals,  it  is  interesting  to 
know  whether  certain  results  of  mathematical  investi- 
gation in  this  direction  might  be  of  practical  value  to 
the  constructor.  In  this  communication  no  reference 
shall  be  made  to  the  dynamical  laws  governing  the 
motion  of  a  bicycle,  but  I  shall  submit  for  practical 
consideration  the  arithmetical  solution  of  a  problem 
which  is  connected  with  the  sprockets  and  chain  of  a 
bicycle,  and  which  may  be  stated  as  follows  : 

What  must  be  the  relation  between  the  number  of 
teeth  of  the  sprockets  and  the  number  of  links  of  the 
chain  in  order  to  have  a  continuous  change  between 


NATURAL    SCIENCE. 


105 


Introduction  to  Chemical  Science. 

By  R.  P.  WILLIAMS,  Instructor  in  Chemistry  in  the  English  High 
School,  Boston.  12mo.  Cloth.  216  pages.  By  mail,  90  cents;  for 
introduction,  80  cents. 

S  work  is  strictly,  but  easily,  inductive.  The  pupil  is  stimu- 
lated by  query  and  suggestion  to  observe  important  phenomena, 
and  to  draw  correct  conclusions.  The  experiments  are  illustrative, 
the  apparatus  is  simple  and  easily  made.  The  nomenclature, 
symbols,,  and  writing  of  equations  are  made  prominent  features. 
In  descriptive  and  theoretical  chemistry,  the  arrangement  of  sub- 
jects is  believed  to  be  especially  superior  in  that  it  presents,  not 
a  mere  aggregation  of  facts,  but  the  science  of  chemistry.  Brev- 
ity and  concentration,  induction,  clearness,  accuracy,  and  a  legiti- 
mate regard  for  interest,  are  leading  characteristics.  The  treat- 
ment is  full  enough  for  any  high  school  or  academy. 

Though  the  method  is  an  advanced  one,  it  has  been  so  simplified 
that  pupils  experience  no  difficulty,  but  rather  an  added  interest, 
in  following  it. 

The  author  himself  has  successfully  employed  this  method  in 
classes  so  large  that  the  simplest  and  most  practical  plan  has 
been  a  necessity. 

Thomas  C.  Van  Nuys,  Professor 


of  Chemistry,  Indiana  University, 
Bloomington,  2nd. :  1  consider  it  an 
excellent  work  for  students  entering 
upon  the  study  of  chemistry. 

C.  F.  Adams,  Teacher  of  Science, 
High  School,  Detroit,  Mich. :  I  have 
carried  two  classes  through  Wil- 
liams's  Chemistry.  The  book  has 
surpassed  my  highest  expectations. 
It  gives  greater  satisfaction  with 
each  succeeding  class. 

J.  W.  Simmons,  County  Superin- 
tendent of  Schools,  Owosso,  Mich.  : 
The  proof  of  the  merits  of  a  text- 
book, is  found  in  the  crucible  of  the 
class-room  work.  There  are  many 
chemistries,  and  good  ones ;  but,  for 
our  use,  this  leads  them  all.  It  is 
stated  in  language  plain,  interesting 
and  not  misleading.  A  logical  order 
is  followed,  and  the  mind  of  the 


student  is  at  work  because  of  the 
many  suggestions  offered.  We  use 
Williams's  work,  and  the  results  are 
all  we  could  wish.  There  is  plenty 
of  chemistry  in  the  work  for  any  of 
our  high  schools. 

W.  J.  Martin,  Professor  of  Chem- 
ist)-}/, Davidson  College,  N.C. :  One 
of  the  most  admirable  little  text- 
books I  have  ever  seen. 

T.  H.  Norton,  Professor  of  Chem- 
istry, Cincinnati  University,  0. :  Its 
clearness,  accuracy,  and  compact 
form  render  it  exceptionally  well 
adapted  for  use  in  high  and  prepara- 
tory schools.  I  shall  warmly  recom- 
mend it  for  use,  whenever  the  effort 
is  made  to  provide  satisfactory  train- 
ing in  accordance  with  the  require- 
ments for  admission  to  the  scientific 
courses  of  the  University. 


106 


NATURAL   SCIENCE. 


Laboratory  Manual  of  General  Chemistry. 

'By  R.  P.  WILLIAMS,  Instructor  in  Chemistry,  English  High  School, 
Boston.  12mo.  Boards,  xvi  +  200  pages.  By  mail,  30  cents ;  for  intro- 
duction, 25  cents. 

fPHE  book  contains  one  hundred  experiments  in  general  chem- 
istry arid  qualitative  analysis,  blanks  opposite  each  for  pupils 
to  take  notes,  laboratory  rules,  complete  tables  of  symbols,  with 
chemical  and  common  names,  reagents,  solutions,  chemicals,  and 
apparatus,  and  the  plan  of  a  model  laboratory.  Minute  directions, 
and  suggestions  designed  to  help  the  pupils  observe  and  draw 
inferences,  characterize  each  experiment. 

An  Elementary  Chemistry. 

By  GEORGE  R.  WHITE,  Instructor  in  Chemistry  at  Phillips  Academy, 
Exeter.  12mo.  Cloth,  xxix  +  272  pages.  Mailing  price,  $1.10;  for 
introduction,  $1.00. 

HPHIS  is  an  excellent  text-book  for  High  Schools  and  Academies, 
and  for  elementary  classes  in  Colleges.  The  strictly  inductive 
method  here  followed,  together  with  the  insertion  of  numerous 
questions  that  must  cause  the  student  to  do  his  own  reasoning 
from  the  observations,  renders  this  book  particularly  useful. 

The  experiments,  which  have  all  been  well  tried  and  found  to 
work  successfully,  are  well  adapted  to  the  needs  of  students.  The 
laboratory  fittings  and  apparatus  called  for  are  of  the  simplest 
and  most  inexpensive  kind. 

0.  P.  Watts,  Instructor  of  Mathe- 
matics and  Science,  Franklin  Col- 
lege, Malone,  N.  Y. :  The  best  intro- 
duction to  general  chemistry  by  the 
laboratory  method  that  I  have  ever 
seen.  It  is  explicit  and  practical,  — 
a  book  sure  to  make  eager,  clear, 
and  scientific  students. 

T.  H.  Norton,  Professor  of  Chem- 
istry, University  of  Cincinnati,  Cin- 
cinnati, Ohio :  I  am  greatly  pleased 
with  the  plan  and  its  execution.  It 
is  an  admirable  arrangement  for  our 
inductive  course  in  chemistry  and 
should  not  fail  to  yield  good  results. 


H.  N.  Howland,  Teacher  of  Phys- 
ics and  Chemistry,  High  School, 
Rockford,  III. :  I  have  been  looking 
for  some  time  for  a  satisfactory 
book  to  use  in  our  laboratory  and  am 
pleased  to  say  that  this  one  suits  me 
better  than  anything  I  have  seen  yet. 

Edw.  K.  Evans,  Principal  of  High 
School,  Amherst,  Mass.:  It  is  the 
best  book  of  the  kind  I  have  ever 
seen.  I  thoroughly  believe  in  the 
general  plan  of  the  book,  the  "  In- 
ductive Method"  —  believing  it  to 
be  by  far  the  most  rational  and  truly 
practical  method. 


NATURAL   SCIENCE. 


107 


Young's  Lessons  in  Astronomy. 

Including  Uranography.  By  CHARLES  A.  YOUNG,  Ph.D.,  LL.D.,  Pro- 
fessor of  Astronomy  in  Princeton  University,  and  author  of  A  General 
Astronomy,  Elements  of  Astronomy,  etc.  12mo.  Cloth.  Illustrated, 
ix  +  357  pages,  exclusive  of  four  double-page  star  maps.  By  mail, 
$1.30;  for  introduction,  $1.20 


volume  has  been  prepared  for  schools  that  desire  a  brief 
course  free  from  mathematics.  It  is  based  upon  the  author's 
Elements  of  Astronomy,  but  many  condensations,  simplifications, 
and  changes  of  arrangement  have  been  made.  In  fact,  everything 
has  been  carefully  worked  over  and  rewritten  to  adapt  it  to  the 
special  requirements.  Great  pains  has  been  taken  not  to  sacrifice 
accuracy  and  truth  to  brevity,  and  no  less  to  bring  everything 
thoroughly  down  to  date.  The  latest  results  of  astronomical  in- 
vestigation will  be  found  here.  The  author  has  endeavored,  too, 
while  discarding  mathematics,  to  give  the  student  a  clear  under- 
standing and  a  good  grasp  of  the  subject.  As  a  body  of  informa- 
tion and  as  a  means  of  discipline,  this  book  will  be  found,  it  is 
believed,  of  notable  value.  The  most  important  change  in  the 
arrangement  of  the  book  has  been  in  bringing  the  Uranography, 
or  constellation  tracing,  into  the  body  of  the  text  and  placing  it 
near  the  beginning,  a  change  in  harmony  with  the  accepted  prin- 
ciple that  those  whose  minds  are  not  mature  succeed  best  in  the 
study  of  a  new  subject  by  beginning  with  what  is  concrete  and 
appeals  to  the  senses,  rather  than  with  the  abstract  principles. 
Brief  notes  on  the  legendary  mythology  of  the  constellations  have 
been  added  for  the  benefit  of  such  pupils  as  are  not  likely  to 
become  familiar  with  it  in  the  study  of  classical  literature. 


M.  W.  Harrington,  Chief  of  U.  S. 
Weather  Bureau,  Washington,  D.C. : 
I  have  been  much  pleased  in  looking 
it  over,  and  will  take  pleasure  in 
commending  it  to  schools  consulting 
me  and  requiring  an  astronomy  of 
this  grade.  The  whole  series  of  As- 
tronomies reflects  credit  on  their 
distinguished  author  and  shows  that 
he  appreciates  the  needs  of  the 
schools. 


Clarence  E.  Kelley,  Prin.  of  High 
School,  Haverhill,  Mass. :  It  seems 
to  me  the  book  is  admirably  adapted 
to  its  purpose,  and  that  it  accom- 
plishes the  difficult  task  of  present- 
ing to  the  student  or  reader  not 
conversant  with  Algebra  and  Geom- 
etry, an  excellent  selection  of  what 
may  with  profit  be  given  him  as  an 
introduction  to  the  science  of  astron- 
omy. 


NATURAL    SCIENCE.  Ill 

Blaisdell's  Physiologies. 

By  ALBERT  F.  BLAISDELL,  M.D. 
The  Child's  Book  of  Health. 

Revised  Edition.  In  easy  lessons  for  schools.  Illustrated.  Mailing 
price,  35  cents;  for  introduction,  30  cents. 

How  to  Keep  Well. 

Revised  Edition.  A  text-book  of  health  for  use  in  the  lower  grade  of 
schools.  Mailing  price,  55  cents;  for  introduction,  45  cents. 

Our  Bodies  and  How  We  Live. 

Revised  Edition.  A  text-book  of  physiology  and  hygiene  adapted  for 
use  in  advanced  grammar  schools  and  high  schools.  12mo.  Cloth, 
vi  +  403  pages.  Mailing  price,  75  cents ;  for  introduction,  65  cents. 

How  to  Teach  Physiology.  A  Handbook  for  Teachers.  10  cents. 
gLAISDELL'S  PHYSIOLOGIES  are  true,  scientific,  interesting, 
and  teachable.  The  matter  is  fresh  and  to  a  considerable 
extent  new.  The  language  is  clear,  terse,  and  suggestive.  Special 
emphasis  is  laid  upon  the  personal  care  of  health.  Special  refer- 
ence is  made  throughout  the  series  to  the  effects  of  alcoholic 
drinks,  tobacco  and  other  narcotics  on  the  human  system.  Im- 
portant principles  are  illustrated  by  a  systematic  series  of  simple 
experiments.  This  feature  is  peculiar  to  the  Blaisdell  books  arid 
has  been  found  no  less  valuable  than  original. 


teach  it;  they  are  full  of  practical 
suggestions  and  aids  to  instruction, 
and  are  thoroughly  satisfactory  from 
every  standpoint. 


H.  S.  Tarbell,  Superintendent  of 
Schools,  Providence,  R.I. :  Blais- 
dell's Physiologies  were  written  by 
a  scholar  and  a  teacher ;  by  one  who 
knows  his  subject  and  knows  how  to 

A  Hygienic  Physiology. 

For  the  Use  of  Schools.  By  D.  F.  LINCOLN,  M.D.  12mo.  Cloth. 
Illustrated.  v  + 206  pages.  Mailing  price,  90  cents;  for  introduction, 
80  cents. 

TT  is  the  distinctive  feature  of  this  book  to  put  hygiene  first  and 
make  anatomy  and  physiology  tributary  instead  of  making 
anatomy  and  physiology  the  main  things  and  introducing  hygiene 
incidentally. 

An  Epitome  of  Anatomy,  Physiology,  and  Hy- 

giene. — Including  the  Effects  of  Alcohol  and  Tobacco. 

By  H.  H.  CULVER,  formerly  Teacher  of  Physiology  in  Bishop  College, 
Marshall,  Texas.  8vo.  Boards.  22  pages.  Mailing  price,  25  cents ;  for 
introduction,  20  cents. 


NATURAL    SCIENCE. 


Elementary  Meteorology. 

By  WILLIAM  MORRIS  DAVIS,  Professor  of  Physical  Geography  in  Har- 
vard College.  With  maps  and  charts.  8vo.  Cloth,  xi  +  355  pages. 
Mailing  price,  $2.70;  for  introduction,  $2.50. 

work  is  believed  to  be  very  opportune,  since  no  elementary 
work  on  the  subject  has  been  issued  for  over  a  quarter  of  a 
century.  It  represents  the  modern  aspects  of  the  science.  It  is 
adapted  to  the  use  of  students  in  high  schools,  academies,  and 
colleges,  who  have  already  some  knowledge  of  elementary  physics, 
and  who  wish  to  gain  a  general  understanding  of  the  processes  of 
the  atmosphere.  It  will  meet  the  needs  of  members  of  the 
National  and  State  Weather  Services  who  wish  to  -acquaint  them- 
selves with  something  more  than  methods  of  observation. 

The  essential  theories  of  modern  Meteorology  are  presented  in 
such  form  that  the  student  shall  perceive  their  logical  connection, 
and  shall  derive  from  their  mastery  something  01  the  intellectual 
training  that  comes  with  the  grasp  of  well-tested  conclusions. 

The  charts  of  temperature,  pressure,  winds,  etc.,  are  reduced 
from  the  latest  available  sources,  while  the  diagrams  freely  intro- 
duced through  the  text  are  for  the  most  part  new. 


A.  W.  Greeley,  retired  Brigadier 
General  U.S.A.,  and  formerly  Chief 
of  Signal  Office,  Washington :  A 
valuable  and  timely  contribution  to 
scientific  text-books. 

Winslow  Upton,  Professor  of  As- 
tronomy, Brown  University :  The 
best  general  book  on  the  subject  in 
our  language. 


Wm.  B.  Clark,  Professor  of  Geol- 
ogy, Johns  Hopkins  University :  An 
excellent  book  and  of  great  value  to 
the  teacher  of  meteorology. 

David  Todd,  Professor  of  Astron- 
omy, Amherst  College:  Clear,  con- 
cise, and  direct.  To  teach  meteorol- 
ogy with  it  must  be  a  delight. 


The  American  Meteorological  Journal. 

A  Monthly  Review  of  Meteorology. 

Edited  by  ROBERT  DEC.  WARD,  Harvard  University, Cambridge, Mass. 
Contributing  Editors.  —  MARK  W.  HARRINGTON,  Chief  of  the  United 
States  Weather  Bureau  ;  A.  LAWRENCE  ROTCH,  Proprietor  of  the  Blue 
Hill  Observatory,  Massachusetts  :  Prof.  CLEVELAND  ABBE,  United 
States  Weather  Bureau,  Washington,  D.C. ;  Prof.  WILLIAM  M.  DAVIS, 
Harvard  University,  Cambridge,  Mass.  Crown  8vo.  About  40  pages 
in  each  number.  Annual  subscription,  $3.00;  single  number,  30  cents. 

A  LMOST  indispensable  to  all  who  are  interested  in  the  science 
of  meteorology,  climatology,  and  kindred  subjects. 


NATURAL   SCIENCE. 


109 


Young's  General  Astronomy. 

A  Text-book  for  Colleges  and  Technical  Schools.  By  CHARLES  A. 
YOUNG,  Ph.D.,  LL.D.,  Professor  of  Astronomy  in  Princeton  University, 
and  author  of  The  Sun,  etc.  8vo.  viii  +  551  pages.  Half  morocco. 
Illustrated  with  over  250  cuts  and  diagrams,  and  supplemented  with  the 
necessary  tables.  Price  by  mail,  $2.50;  for  introduction,  $2.25. 

TN  amount,  the  work  has  been  adjusted  as  closely  as  possible  to 
the  prevailing  courses  of  study  in  our  colleges.     By  omitting 
the  fine  print,  a  briefer  course  may  be  arranged. 

The  eminence  of  Professor  Young  as  an  original  investigator 
in  astronomy,  a  lecturer  and  writer,  on  the  subject,  and  an. 
instructor  of  college  classes,  and  his  scrupulous  care  in  preparing 
this  volume,  led  the  publishers  to  present  the  work  with  the 
highest  confidence  ;  and  this  confidence  has  been  fully  justified 
by  the  event.  More  than  one  hundred  colleges  adopted  the  work 
within  a  year  from  its  publication,  and  it  is  conceded  to  be  the 
best  astronomical  text-book  of  its  grade  to  be  found  anywhere. 

Edw.  C,  Pickering,  Prof,  of  As-\     S.  P.  Langley,  Sec.  Smithsonian 
tronomy,    Harvard     University:     Iilnst.,  Washington,  I). C. :  I  know  no 


think  this  work  the  best  of  its  kind, 
and  admirably  adapted  to  its  pur- 
pose. 


better  book  (not  to  say  as  good  £ 
one)  for  its  purpose,  on  the  subject. 


An  Introduction  to  Spherical  and  Practical  As- 

tronomy. 

By  DASCOM  GREENE,  Professor  of  Mathematics  and  Astronomy  in  the 
Kensselaer  Polytechnic  Institute,  Troy,  N.  Y.  8vo.  Cloth.  Illustrated, 
viii  +  158  pages.  Mailing  price,  $1.60 ;  for  introduction,  $1.50. 

rpHE  book  is  intended  for  class-room  use  and  affords  such  a  prep- 
aration as  the  student  needs  before  entering  upon  the  study 
of  the  larger  and  more  elaborate  works  on  this  subject. 

The  appendix  contains  an  elementary  exposition  of  the  method 
of  least  squares. 

Daniel  Carhart,  Act.  Prof.  Math-  Kodney  G.  Kimball,  Polytechnic 
ematics,  Western  Univ.  of  Pa..  Alle-  Institute,  Brooklyn,  N.Y.:  The 
gheny,  Pa. :  Professor  Greene  has  hasty  examination  which  I  have 
supplied  that  which  is  needed  to  make  given  it  has  left  a  very  favorable 
the  usual  course  in  Astronomy  in  our  impression  as  to  its  merits  as  a 
colleges  more  practical.  judicious  compound  of  the  practical 

work  which  it  professes  to  cover. 


110  NATURAL   SCIENCE. 

Schemer's  Astronomical  Spectroscopy. 

Department  of  Special  Publication.  —  Translated,  revised  and  en- 
larged by  E.  B.  FROST,  Associate  Professor  of  Astronomy  in  Dart- 
mouth College.  8vo.  Half  leather.  Illustrated,  xiii  +  482  4-  pages* 
Price  by  mail,  $5.00;  for  introduction,  $4.75. 

work  aims  to  explain  the  most  practical  and  modern 
methods  of  research,  and  to  state  our  present  knowledge  of 
the  constitution,  physical  condition  and  motions  of  the  heavenly 
bodies,  as  revealed  by  the  spectroscope. 

There  are  three  parts  :  —  I.  Spectroscopic  Apparatus  ;  II.  Spec- 
tral Theories ;  III.  Results  of  Spectroscopic  Observations,  with  a 
fourth  containing  tables  of  wave-lengths  of  lines  of  the  solar 
spectrum,  catalogues  of  stars  with  special  types  of  spectra,  and  a 
full  bibliography  brought  down  to  1893. 


EdwardS.  Holden,  Director  of  the 
Lick  Observatory,  Mt.  Hamilton, 
California:  I  congratulate  you  on 
the  appearance  of  this  very  impor- 
tant book;  it  is  indispensable  to 


all    astronomers    and    students   of 
spectroscopy. 

W.  W.  Campbell,  Astronomer, 
Lick  Observatory,  University  of 
California:  I  have  only  words  of 
praise  to  bestow  upon  the  book. 

Elements  of  Structural  and  Systematic  Botany. 

For  High  Schools  and  Elementary  College  Courses.  By  DOUGLAS  H. 
CAMPBELL,  Professor  of  Botany  in  the  Leland  Stanford  Junior  Univer- 
sity. 12mo.  Cloth.  ix  +  253  pages.  Price  by  mail,  $1.25  :  for  intro- 
duction, $1.12. 


fundamental  peculiarity  and  merit  of  this  'book  is  that  it 
begins  with  the  simple  forms,  and  follows  the  order  of  nature 
to  the  complex  ones. 


teclmic  with  a  logical  treatment  of 
the  more  minute  structure  of  plants, 
to  render  it  a  help  to  the  teacher  of 
to-day. 


E.  Ellsworth  Call,  Teacher  of 
Natural  Science,  High  School,  West 
Des  Moines,  la. :  It  is  the  only 
manual  which  combines  just  enough 

Plant  Organization. 

By  R.  HALSTED  WARD,  M.D.,  F.R.M.S.,  Professor  of  Botany  in  the 
Rensselaer  Polytechnic  Institute,  Troy,  N.Y.  Quarto.  176  pages. 
Illustrated.  Flexible  boards.  Mailing  price,  85  cents;  for  introduc- 
tion, 75  cents. 

TT  consists  of  a  synoptical  review  of  the  general  structure  and 
morphology  of  plants,  with  blanks  for  written  exercises  by 
pupils. 


NATURAL    SCIENCE    TEXT-BOOKS. 


Principles  of  Physics.    A  Text-book  for  High  Schools  and  Academies. 

By  ALFRED  P.  GAGE,  Instructor  of  Physics  in  the  English  High 

School,  Boston.     $1.30. 
Elements  of  Physics.    A  Text-book  for  High  Schools  and  Academies. 

By  ALFRED  P.  GAGE.     $1.12. 

Introduction  to  Physical  Science.    By  ALFRED  P.  GAGE.    $1.00. 
Physical  Laboratory  Manual  and  Note-Book.    By  ALFRED  P.  GAGE. 

35  cents. 
Introduction  to  Chemical  Science.    By  R.  P.  WILLIAMS,  Instructor  in 

Chemistry  in  the  English  High  School,  Boston.    80  cents. 
Laboratory  Manual  of  General  Chemistry.  By  R.  P.  WILLIAMS.  25  cents. 
Chemical  Experiments.    General  and  Analytical.    By  R.  P.  WILLIAMS. 

For  the  use  of  students  in  the  laboratory.  [In  press. 

Elementary  Chemistry.    By  GEORGE  R.  WHITE,  Instructor  of  Chemistry, 

Phillips  Exeter  Academy.     $1.00. 
General  Astronomy.    A  Text-book  for  Colleges  and  Technical  Schools. 

By  CHARLES  A.  YOUNG,  Professor  of  Astronomy  in  the  College  of 

New  Jersey,  and  author  of  "The  Sun,"  etc.     $2.25. 
Elements  of  Astronomy.    A  Text-book  for  High  Schools  and  Academies, 

with  a  Urauography.     By  Professor  CHARLES   A.   YOUNG.     $1.40. 

Uranography.     30  cents. 
Lessons  in  Astronomy.   Including  Uranography.   By  Professor  CHARLES 

A.  YOUNG.    Prepared  for  schools  that  desire  a  brief  course  free  from 

mathematics.     $1.20. 
An  Introduction  to  Spherical  and  Practical  Astronomy.    By  DASCOM 

GREENE,  Professor  of  Mathematics  and  Astronomy  in  the  Rensselaer 

Polytechnic  Institute,  Troy,  N.  Y.    $1.50. 
Elements  of  Structural  and  Systematic  Botany.    For  High  Schools  and 

Elementary  College  Courses.    By  DOUGLAS  HOUGHTON  CAMPBELL, 

Professor  of  Botany  in  the  Leland  Stanford  Junior  University.  $1.12. 
A  High  School  Botany.    By  J.  Y.  BERGEN,  Jr.,  Teacher  of  Botany  and 

Physiology  in  the  English  High  School,  Boston.  [In  press. 

Laboratory  Course  in  Physical  Measurements.     By  W.  C.  SABINE, 

Instructor  in  Harvard  University.     $1.25. 
Elementary  Meteorology.   By  WILLIAM  M.  DAVIS,  Professor  of  Physical 

Geography  in  Harvard  University.   With  maps,  charts,  and  exercises. 

$2.50. 
Blaisdell's  Physiologies :  Our  Bodies  and  How  We  Live,  65  cents ;  How  to  Keep 

Well,  45  cents ;  Child's  Book  of  Health,  30  cents. 
A  Hygienic  Physiology.  For  the  Use  of  Schools.  By  D.  F.  LINCOLN,  M.D., 

author  of  "  School  and  Industrial  Hygiene,"  etc.    80  cents. 


Copies  will  be  sent,  postpaid,  to  teachers  for  examina- 
tion on  receipt  of  the  introduction  prices  given  above. 


GINN  &  COMPANY,  Publishers,  Boston,  New  York,  Chicago,  Atlanta, 


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